Math and Arithmetic

# What 2 digit numbers are divisible by 3 but not by 6?

Since 3 is a factor of 6, any number divisible by 6 is also divisible by 3. But since 2 is also a factor of 6, then any number divisible by 6 must also be divisible by 2. This means that any number divisible by 6 is an even number. So if a number is odd and it is divisible by 3, then it is not divisible by 6. For example, 12 is divisible by 3, but since it is even, it is also divisible by 6. But 15 is divisible by 3, and it is odd, so it is not divisible by 6.

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## Related Questions

Starting at 12 and ending at 99, there are 30 two-digit numbers divisible by three.

There are 151 3-digit numbers that are divisible by 6.

There are 300 three digit numbers that are divisible by neither 2 nor 3. There are 999 - 100 + 1 = 900 three digit numbers. 100 &divide; 2 = 50 &rarr; first three digit number divisible by 2 is 50 &times; 2 =100 999 &divide; 2 = 499 r 1 &rarr; last three digit number divisible by 2 is 499 &times; 2 = 998 &rarr; there are 499 - 50 + 1 = 450 three digit numbers divisible by 2. 100 &divide; 3 = 33 r 1 &rarr; first three digit number divisible by 3 is 34 &times; 3 = 102 999 &divide; 3 = 333 &rarr; last three digit number divisible by 3 is 333 &times; 3 = 999 &rarr; there are 333 - 34 + 1 = 300 three digit numbers divisible by 3. The lowest common multiple of 2 and 3 is 6, so these have been counted in both those divisible by 2 and those divisible by 3. 100 &divide; 6 = 16 r 4 &rarr; first three digit number divisible by 6 is 17 &times; 6 = 102 999 &divide; 6 = 166 r 3 &rarr; last three digit number divisible by 6 is 166 &times; 6 = 996 &rarr; there are 166 - 17 + 1 = 150 &rarr; there are 450 + 300 - 150 = 600 three digit numbers that are divisible by either 2 or 3 (or both). &rarr; there are 900 - 600 = 300 three digit numbers that are divisible by neither 2 nor 3.

There are 180 3-digit numbers divisible by five.

All whole numbers are divisible by 1. Numbers are divisible by 2 if they end in 2, 4, 6, 8 or 0. Numbers are divisible by 3 if the sum of their digits is divisible by 3. Numbers are divisible by 4 if the last two digits of the number are divisible by 4. Numbers are divisible by 5 if the last digit of the number is either 5 or 0. Numbers are divisible by 6 if they are divisible by 2 and 3. Numbers are divisible by 9 if the sum of their digits is equal to 9 or a multiple of 9. Numbers are divisible by 10 if the last digit of the number is 0.

Last digit (0) is even, so it is divisible by 2 4 + 3 + 2 + 0 = 9 which is divisible by 3, so it is divisible by 3 last digit is 0 or 5, so it is divisible by 5 4 + 3 + 2 + 0 = 9 which is divisible by 9, so it is divisible by 9 last digit is 0, so it is divisible by 10 &rarr; 4320 is divisible by all the numbers 2, 3, 5, 9, 10

48.The first two digit number is 10, the last two digit number is 99, so there are 99 - 10 + 1 = 90 two digit numbers&rarr; 10 &divide; 3 = 31/3 &rarr; first two digit number divisible by 3 is 4 x 3 = 12&rarr; 99 &divide; 3 = 33 &rarr; last two digit number divisible by 3 is 33 x 3 = 99&rarr; 33 - 4 + 1 = 30 two digit numbers divisible by 3&rarr; 10 &divide; 5 = 2 &rarr; first two digit number divisible by 5 is 2 x 5 = 10&rarr; 99 &divide; 5 = 194/5 &rarr; last two digit number divisible by 5 is 19 x 5 = 95&rarr; 19 - 2 + 1 = 18 two digit numbers divisible by 5&rarr; 30 + 18 = 48 two digit numbers divisible by 3 or 5 OR BOTH.The numbers divisible by both are multiples of their lowest common multiple: lcm(3, 5) = 15, and have been counted twice, so need to be subtracted from the total&rarr; 10 &divide; 15 = 010/15 &rarr; first two digit number divisible by 15 is 1 x 15 = 15&rarr; 99 &divide; 15 = 69/15 &rarr; last two digit number divisible by 15 is 6 x 15 = 90&rarr; 6 - 1 + 1 = 6 two digit numbers divisible by 15 (the lcm of 3 and 5)&rarr; 48 - 6 = 42 two digit numbers divisible by 3 or 5.&rarr; 90 - 42 = 48 two digit numbers divisible by neither 3 nor 5.

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.

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

There are 500 such numbers. How about 1818 as an example?

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

between 1 and 600 inclusive there are:300 numbers divisible by 2200 numbers divisible by 3100 numbers divisible by both 2 and 3400 numbers divisible by 2 or 3.

100. The highest 3 digit number divisible by 9 is 999 (111 times). The highest 2 digit number divisible by 9 is 99 (11 times). The difference is 100.

What numbers are only divisible by 2 and 3 .

630 is divisible by...2 or 3 or 5 or 6 or 7 or 9. your welcome

To calculate the 2 digit numbers divisible by 19, you simply start out by multiplying 19 by 2, then by 3, etc., until you reach a number that is 99 or less. The reason you have do it until you reach a number that is 99 is because after 99 you have a 3 digit number. 19 x 2 = 36 19 x 3 = 57 19 x 4 = 76 19 x 5 = 95 So, the 2 digit numbers divisible by 19 are 36, 57, 76, 95

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 3&acirc;&dagger;&rsquo; 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 3&acirc;&dagger;&rsquo; 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 3&acirc;&dagger;&rsquo; 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 3&acirc;&dagger;&rsquo; 121 is not divisible by either 2 or 3, so it is not divisible by 6

712 is divisible by 2 because the digit at ones place is an even number. 712 is not divisible by 3 because the sum of the numbers(7+1+2=10) is not divisible by 3. 712 is divisible by 4 as the last two digits(12) are divisible by 4. 712 is not divisible by 5 because the last digit is neither 5 nor 0. 712 is not divisible by 6 because it is not divisible by 3. 712 is not divisible by 10 because the last digit is not 0.

The smallest 3-digit multiple of 7 is 105 = 15*7 The largest 3-digit multiple of 7 is 994 = 142*7 So there are 142-14 = 128 3-digit multiples of 7, ie 128 3-digit numbers that are divisible by 7.

All numbers divisible by 5 (of which 15 is a multiple) have a final digit of 0 or 5. All numbers divisible by 3 (of which 15 is a multiple) have the sum of the digits totalling 3 or a multiple of 3. Therefore, a number is divisible by 15 if the sum of its digits total 3 or a multiple of 3 and its final digit is 0 or 5. Example : 32085 ; 3 + 2 + 0 + 8 + 5 = 18 which is divisible by 3. Final digit 5. This number is divisible by 15. (32085 &divide; 15 = 2139) 7420 : 7 + 4 + 2 + 0 = 13. This number is not divisible by 15.

There are no single-digit numbers divisible by 630. 630 is divisible by 1, 2, 3, 5, 6, 7 and 9.

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