If a number is divisible by six, then it must also be divisible by both two and three. To check it then, you simply apply both rules for each of those:
Is it an even number?
Is the sum of it's digits divisible by three?
If both answers are yes, then the number is divisible by six.
To find out if a number is divisible by seven take it's last digit, double it, and subtract it from the remaining digits. If the result is divisible by seven, then the original number is as well.
For example is three 343 divisible by 7? Let's find out:
3 * 2 = 6, and 34 - 6 = 28. Is 28 divisible by seven? Yes, but if you're not sure, you can repeat the process. 8 * 2 = 16, 2 - 16 = -14. 14 is of course divisible by 7.
If the last three digits of a number are divisible by 8, then the entire number is. For example, I know that 10923485710234985723908471859256 is divisible by eight, because I know that the last three digits, 256, form a number that's divisible by eight. Not sure about those last three digits? Simply divide them by two, three times in a row. If the result is a whole number, then it's divisible by eight. 256 / 2 = 128, 128 / 2 = 64, 64 / 2 = 32, so 256 is divisible by eight, and therefore 10923485710234985723908471859256 is also.
If the sum of the digits is divisible by 9, then the number itself is. For example, is 8936523 divisible by 9? Well, 8 + 9 + 3 + 6 + 5 + 2 + 3 = 36. Is 36 divisible by 9? 3 + 6 = 9. 9 is obviously divisible by 9, so yes, 8936523 is also.
If the last digit is a zero, then the number is divisible by 10. For example, 12340 is divisible by ten, but 12345 is not.
For any practical purpose, it is easier to simply divide, instead of looking for fancy divisibility rules. However, you can apply the divisibility rules for 3 and for 7. This works because (a) their product is 21, and (b) these numbers are relatively prime.
(3/10) / (7/6) = (3/10) *(6/7) = 18/70 = 9/35(3/10) / (7/6) = (3/10) *(6/7) = 18/70 = 9/35(3/10) / (7/6) = (3/10) *(6/7) = 18/70 = 9/35(3/10) / (7/6) = (3/10) *(6/7) = 18/70 = 9/35
Take the last digit and add 7 times to the rest of the number. Ex: 5888 588+ (7x8)=644, 644/23= 28
By the rules of divisibility, you know that 35 is divisible by 1 and 5 and not divisible by 2, 3, 4 and 6. Dividing those two numbers into 35 gives you 7 and 35. That makes the factors of 35 (1, 5, 7, 35) Now pair them up. (35,1)(7,5)
A number is a multiple of 42 if it's a multiple of 2 and 21 at the same time 126 is a multiple of 42 because it ends in 6, which means it's a multiple of 2, and 12 - 6 x 2 = 0, which means it's a multiple of 21
3+7=10
A number is a multiple of 42 if it's a multiple of 2 and 21 at the same time 126 is a multiple of 42 because it ends in 6, which means it's a multiple of 2, and 12 - 6 x 2 = 0, which means it's a multiple of 21
1: Every number is a multiple of 1 2: The number ends in 0, 2, 4, 6 or 8 3: The sum of the digits is a multiple of 3 4: The last 2 digits are a multiple of 4 The 10s digit is even and the last digit is 0, 4 or 8 The 10s digit is odd and the last digit is 2 or 6 5: The number ends in 0 or 5 6: The number is a multiple of 2 and 3 at the same time 7: The difference between twice the last digit and the rest of the number is a multiple of 7 8: The last 3 digits are a multiple of 8 The 100s digit is even and the last 2 digits are a multiple of 8 The 100s digit is odd and the last 2 digits are 4 times an odd number 9: The sum of the digits is a multiple of 9 10: The number ends in 0 11: The difference between the last digit and the rest of the number is a multiple of 11 12: The number is a multiple of 3 and 4 at the same time 13: The sum of 4 times the last digit and the rest of the number is a multiple of 13 14: The number is a multiple of 2 and 7 at the same time 15: The number is a multiple of 3 and 5 at the same time 16: The last 4 digits are a multiple of 16 The 1,000s digit is even and the last 3 digits are a multiple of 16 The 1,000s digit is odd and the last 3 digits are 8 times an odd number 17: The difference between 5 times the last digit and the rest of the number is a multiple of 17 18: The number is a multiple of 2 and 9 at the same time 19: The sum of twice the last digit and the rest of the number is a multiple of 19 20: The number ends in 00, 20, 40, 60 or 80 21: The difference between twice the last digit and the rest of the number is a multiple of 21 22: The number is a multiple of 2 and 11 at the same time 23: The sum of 7 times the last digit and the rest of the number is a multiple of 23 24: The number is a multiple of 3 and 8 at the same time 25: The number ends in 00, 25, 50 or 75 26: The number is a multiple of 2 and 13 at the same time 27: The difference between 8 times the last digit and the rest of the number is a multiple of 27 28: The number is a multiple of 4 and 7 at the same time 29: The sum of thrice the last digit and the rest of the number is a multiple of 29 30: The number is a multiple of 3 and 10 at the same time 31: The difference between thrice the last digit and the rest of the number is a multiple of 31 32: The last 5 digits are a multiple of 32 The 10,000s digit is even and the last 4 digits are a multiple of 32 The 10,000s digit is odd and the last 4 digits are 16 times an odd number 33: The sum of 10 times the last digit and the rest of the number is a multiple of 33 34: The number is a multiple of 2 and 17 at the same time 35: The number is a multiple of 5 and 7 at the same time 36: The number is a multiple of 4 and 9 at the same time 37: The difference between 11 times the last digit and the rest of the number is a multiple of 37 38: The number is a multiple of 2 and 19 at the same time 39: The sum of 4 times the last digit and the rest of the number is a multiple of 39 40: The last 3 digits are a multiple of 40 The 100s digit is even and the last 2 digits are 00, 40 or 80 The 100s digit is odd and the last 2 digits are 20 or 60 41: The difference between 4 times the last digit and the rest of the number is a multiple of 41 42: The number is a multiple of 2 and 21 at the same time 43: The sum of 13 times the last digit and the rest of the number is a multiple of 43 44: The number is a multiple of 4 and 11 at the same time 45: The number is a multiple of 5 and 9 at the same time 46: The number is a multiple of 2 and 23 at the same time 47: The difference between 14 times the last digit and the rest of the number is a multiple of 47 48: The number is a multiple of 3 and 16 at the same time 49: The sum of 5 times the last digit and the rest of the number is a multiple of 49 50: The number ends in 00 or 50
It is: 7
For any practical purpose, it is easier to simply divide, instead of looking for fancy divisibility rules. However, you can apply the divisibility rules for 3 and for 7. This works because (a) their product is 21, and (b) these numbers are relatively prime.
If the last digit doubled subtracted from the rest is a multiple of 7, the whole number is divisible by 7.
The square root of 53 is between 7 and 8. If 53 was composite, half of its factors would be less than its square root. By the rules of divisibility, we know that 53 is not divisible, by 2, 3, 4, 5, 6 or 7. It has to be prime.
(3/10) / (7/6) = (3/10) *(6/7) = 18/70 = 9/35(3/10) / (7/6) = (3/10) *(6/7) = 18/70 = 9/35(3/10) / (7/6) = (3/10) *(6/7) = 18/70 = 9/35(3/10) / (7/6) = (3/10) *(6/7) = 18/70 = 9/35
You know that the square root of 100 is 10, so half the remaining factors will be greater than 10, half lesser. By the rules of divisibility, you know that 100 is not divisible by 3, 6, 7, 8 or 9. That leaves 1, 2, 4 and 5. Divide them into 100. 1, 2, 4, 5, 10, 20, 25, 50, 100
Take the last digit and add 7 times to the rest of the number. Ex: 5888 588+ (7x8)=644, 644/23= 28
spell out the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in English then alphabetize them.
7 is only divisible by 1 and itself.