Q: Is a number divisible by 3 if its last digit is divisible by 3?

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no

Converse:If a number is divisible by 3, then every number of a digit is divisible by three. Inverse: If every digit of a number is not divisible by 3 then the number is not divisible by 3? Contrapositive:If a number is not divisible by 3, then every number of a digit is not divisible by three.

yes 552 is divisible by 6 and the result is 92... to find out if a number is divisible by 6 then that number must be divisible by 2 and 3.. 1.If a number is divisble by three then the last digit must be divisible by 2 (so that the last digit must be 0,2,4,6,8) in this number the last digit is 2 so that it is divisible by 2 2.If a number is divisble by 3 then the sum of its digit must be divisible by 3. In this case the sum of the digits of 552 is 5+5+2= 12 and 12 is divisible by 3.... If this two rules fit in then that number is divisible by 6

a 3 digit number that is divisible by on is a three digit number that is a multiple of one.

All 4 digit numbers that are divisible by 9 are also divisible by 3. The first is 1008 and the last is 9999.

no, as it is an odd number. (3 as the last digit)

The first 3 digit natural number is 100: 100 ÷ 4 = 25 → first 3 digit natural number divisible by 4 is 4 × 25 The last 3 digit natural number is 999: 999 ÷ 4 = 249 r 3 → last 3 digit natural number divisible by 4 is 4 × 249 → number of 3 digit natural numbers divisible by 4 is 249 - 25 + 1 = 225.

144 is divisible by 2, 3, 4, 6, 9 and not divisible by 5 or 10.Divisible by 2The whole number is divisible by 2 if the number is even which is shown by the last digit being divisible by 2. The last digit of 144 is 4 and 4 is divisible by 2, thus 144 is divisible by 2.Divisible by 3The number is divisible by 3 if the sum of its digits is also divisible by 3. Sum of the digits of 144 is 1+4+4 = 9 which is divisible by 3, thus 144 is divisible by 3Divisible by 4The number is divisible by 4 is the last two digits is also divisible by 4. Last two digits of 144 are 44 which are divisible by 4, thus 144 is divisible by 4An alternative test: If the last digit plus twice the preceding digit is divisible by 4 then the whole number is divisible by 4.For 144, last digit + twice preceding digit is 4+2x4 = 12 which is divisible by 4, so 144 is divisible by 4Divisible by 5If the last digit is 0 or 5 then the number is divisible by 5 Last digit of 144 is 4 which is neither 0 nor 5, thus 144 is not divisible by 5Divisible by 6To be divisible by 6, the number must be divisible by both of 2 and 3. 144 is divisible by both 2 and 3 (see above), thus 144 is divisible by 6Divisible by 9If the sum of the digits of the number is divisible by 9, then the original number is divisible by 9. For 144, 1+4+4 = 9 which is divisible by 9, thus 144 is divisible by 9Divisible by 10To be divisible by 10, the last digit must be 0. The last digit of 144 is 4 which is not 0, thus 144 is not divisible by 10

To be divisible by 2 the number must be even, that is its last digit must be 2, 4, 6, 8, or 0; the last digit of 432 is 2 which is one of {2, 4, 6, 8, 0} so 432 is even and divisible by 2. To be divisible by 3 sum the digits of the number; if this sum is divisible by 3 then the original number is divisible by 3. The test can be repeated on the sum until a single digit remains, in which case if this single digit is 3, 6, or 9 then the original number is divisible by 3; For 432: 4 + 3 + 2 = 9 which is one of {3, 6, 9} so 432 is divisible by 3. To be divisible by 5 the last digit must be a 0 or 5; the last digit of 432 is a 2 which is not 0 nor 5, so 432 is not divisible by 5. To be divisible by 6, the number must be divisible by both 2 and 3; these have been tested above and found to be true, so 432 is divisible by 6. To be divisible by 9 sum the digits of the number; if this sum is divisible by 9 then the original number is divisible by 9. The test can be repeated on the sum until a single digit remains, in which case if this single digit is 9 then the original number is divisible by 9; For 432: 4 + 3 + 2 = 9 which is 9 so 432 is divisible by 9 To be divisible by 10 the last digit must be a 0; the last digit of 432 is a 2 which is not 0, so 432 is not divisible by 10. 432 is divisible by 2, 3, 6 and 9, but not divisible by 5 nor 10.

The divisible rule for 2 is if the last digit of the number is 0,2,4,6, or 8. The divisible rule for 3 is if the last 2 digits of the number is divisible by 3,03,06,09,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96, or 99.

The first 3 digit number divisible by 19 is 114 (= 19 x 6) The last 3 digit number divisible by 19 is 988 (= 19 x 52) That means that there are 52 - 6 + 1 = 47 three digit numbers that are divisible by 19.

the number 3 is divisible by 3

To be divisible by 6, the number must be divisible by both 2 and 3:To be divisible by 2 the last digit must be even, ie one of {0, 2, 4, 6, 8};To be divisible by 3, sum the digits of the number and if this sum is divisible by 3, then the original number is divisible by 3.As the test can be repeated on the sum, repeat the summing until a single digit remains; only if this number is one of {3, 6, 9} is the original number divisible by 3.If the number is not divisible by 2 or 3 (or both) then the number is not divisible by 6.examples:126Last digit is even so it is divisible by 2 1 + 2 + 6 = 9 which is divisible by 3, so it is divisible by 3â†’ 126 is divisible by both 2 and 3, so it is divisible by 6124Last digit is even so it is divisible by 2 1 + 2 + 4 = 7 which is not divisible by 3, so it is not divisible by 3â†’ 126 is divisible by 2 but not divisible by 3, so it is not divisible by 6123Last digit is not even so it is not divisible by 2 We can stop at this point as regardless of whether it is divisible by 3 or not, it will not be divisible by 6. However, for completeness:1 + 2 + 3 = 6 which is divisible by 3, so it is divisible by 3â†’ 123 is divisible by 3 but not divisible by 2, so it is not divisible by 6121Last digit is not even so it is not divisible by 2 We can stop at this point as regardless of whether it is divisible by 3 or not, it will not be divisible by 6. However, for completeness:1 + 2 + 1 = 4 which is not divisible by 3, so it is not divisible by 3â†’ 121 is not divisible by either 2 or 3, so it is not divisible by 6

To be divisible by 2 the number must be even, that is its last digit must be 2, 4, 6, 8, or 0; the last digit of 26 is 6 which is one of {2, 4, 6, 8, 0} so 26 is even and divisible by 2. To be divisible by 3 sum the digits of the number; if this sum is divisible by 3 then the original number is divisible by 3. The test can be repeated on the sum until a single digit remains, in which case if this single digit is 3, 6, or 9 then the original number is divisible by 3; For 26: 2 + 6 = 8 which is not one of {3, 6, 9} so 26 is not divisible by 3. To be divisible by 5 the last digit must be a 0 or 5; the last digit of 26 is a 6 which is not 0 nor 5, so 26 is not divisible by 5. To be divisible by 9 sum the digits of the number; if this sum is divisible by 9 then the original number is divisible by 9. The test can be repeated on the sum until a single digit remains, in which case if this single digit is 9 then the original number is divisible by 9; For 26: 2 + 6 = 8 which is not 9 so 26 is not divisible by 9. 26 is divisible by 2 but not divisible by 3, 5 nor 9.

The only 3-digit number that is divisible by 624 is 624.

305 can only be [exactly] divided by 5 and not 2, 3, 6, 9 nor 10.Divisibility tests:2: NoNumber must be even (last digit divisible by 2). Last digit is 5 which is not even, so the whole number (305) not divisible by 2.3: NoAdd up the digits of the number; if this sum is divisible by 3, then the original number is divisible by 3: 3 + 0 + 5 = 8 which is not divisible by 3, so the original number (305) is not divisible by 3.5: YesLast digit is 0 or 5. Last digit is 5, so 305 is divisible by 5. 6: No6 = 2 x 3, so number must pass both tests for divisibility of 2 and 3; 305 fails tests for (both) 2 and 3 (above), so is not divisible by 6. 9: NoAdd up the digits of the number; if this sum is divisible by 9, then the original number is divisible by 9: 3 + 0 + 5 = 8 which is not divisible by 9, so the original number (305) is not divisible by 9.10: NoThe last digit of the number must be 0. Last digit is 5, so 305 is not divisible by 10.

21 is not divisible by 2 nor 5, but it is divisible by 3. To be divisible by 2 the last digit must be even (one of {0, 2, 4, 6, 8}; the last digit 1 is not one of these, thus 21 is not divisible by 2 To be divisible by 3 sum the digits and if this total is divisible by 3, then so is the original number; the test can be repeated on the sum, so by repeatedly summing the digits of the totals until a single digit remains only if that single digit is 3, 6 or 9 is the original number divisible by 3. 21 → 2 + 1 = 3 which is divisible by 3 so 21 is divisible by 3. To be divisible by 5, the last digit must be 0 or 5. The last digit of 21 is 1 which is not 0 nor 5, thus 21 is not divisible by 5.

999 is divisible by 9, but not by six; the next lower number divisible by 9 is 990, which is also divisible by 6, so that's the answer. Some shortcuts for divisibility: 0 is divisible by any number. If the last digit of a number is divisible by 2, the number itself is divisible by 2. If the sum of the digits of a number is divisible by 3, the number itself is divisible by 3. If the last TWO digits of a number are divisible by 4, the number itself is divisible by 4. If the last digit of a number is divisible by 5, the number itself is divisible by 5. If a number is divisible by both 2 and 3, it is divisible by 6. If the last THREE digits of a number are divisible by 8, the number itself is divisible by 8. If the sum of the digits of a number is divisible by 9, the number itself is divisible by 9. 990: 9+9+0=18, which is divisible by 9, so 990 is divisible by 9. 18 is also divisible by 3, so 990 is divisible by 3, and since 990 ends in 0 it's also divisible by 2, meaning that it's divisible by 6 as well.

5715 is not divisible by 2: the last digit is not an even number or 05715 is divisible by 3: as the last two digits when added together is a multiple of 35715 is divisible by 5: as the last digit is a 5 or 05715 is divisible by 9: as if u added all the digits of the number it will be divisible by 9, in this case 5 +7+1+5=18 and 18 is a multiple of 95715 is not divisible by 10: as the last digit is not a 0

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1002 is the smallest 4 digit number divisible by 3 and 2.

To be divisible by 2 the last digit must be even, ie one of {0, 2, 4, 6, 8}; The last digit of 75 is 5, which is not one of these so it is not divisible by 2. To be divisible by 3, sum the digits of the number and if this sum is divisible by 3, then the original number is divisible by 3. As the test can be repeated on the sum, repeat the summing until a single digit remains; only if this number is one of {3, 6, 9} is the original number divisible by 3. For this gives: 75→7 + 5 = 12 12→1 + 2 = 3 3 is one of {3, 6,9} so it is divisible by 3. To be divisible by 4, add the last (ones) digit to twice the previous (tens) digit; if this sum is divisible by 4, then so is the original number. As the test can be repeated on the sum, repeat the summing until a single digit remains; only if this number is one of {4, 8} is the original number divisible by 4. For this gives: 75→5 + 2×7 = 19 19→9 + 2×1 = 11 11→1 + 2×1 = 3 3 is not one of {4, 8} so it is not divisible by 4. To be divisible by 5, the last digit must be one of {0, 5}. The last digit of is 5 which is one of {0, 5} so it is divisible by 5. To be divisible by 9, sum the digits of the number and if this sum is divisible by 9, then the original number is divisible by 9. As the test can be repeated on the sum, repeat the summing until a single digit remains; only if this number is 9 is the original number divisible by 9. For this gives: 75→7 + 5 = 12 12→1 + 2 = 3 3 is not 9 so it is not divisible by 9. To be divisible by 10, the last digit must be 0 The last digit is 5 which is not 0, so it is not divisible by 10. → 75 is divisible by 3 and 5 75 is not divisible by 2, 4, 9, 10

Not necessarily. For example, the number 56 ends in a 6 but is not divisible by six. To check if a number is divisible by six, the number must be divisible by both 2 and 3. To check this, the last digit must be even and the sum of the digits must be divisible by three. If the number meets these conditions, it is in fact divisible by six.

Yes.

There are 180 3-digit numbers divisible by five.