Yes. To check if a number is divisible by 4, if the last 2 digits (as a number) are divisible by 4, so is the original number. 32 = 4 x 8 so as 32 is divisible by 4, so is 211032. An alternative test for 4: add the last digit to twice the preceding digit, and if this sum is divisible by 4 so is the original number. This can be repeated until a single digit remains which must be 4 or 8 (to be divisible by 4) if the original number is divisible by 4. for 211032: 2 + 3x2 = 8 → [single digit 8 which] is divisible by 4, so 211032 is also divisible by 4.
4000
No. To test if a number is divisible by 8: * first all multiples of 8 are even, so the number must be even; * then: add 4 times the hundreds digit to twice the tens digit to the ones digit - if this sum is divisible by 8, then so is the original number. As the test can be applied to the sum, repeating this summing until a single digit remains, only if this single digit is 8 is the original number divisible by 8. For 100: 4x1 + 2x0 + 0 = 4 which is not 8, so 100 is not divisible by 8.
10001000/8 = 125
2400
If the last two digits are divisible by 4 then the number is divisible by 4. Thus, if the tens digit is even and the units digit is 0 or 4 or 8 OR if the tens digit is odd and the units digit is 2 or 6 then the number is divisible by 4.
Yes. To check if a number is divisible by 4, if the last 2 digits (as a number) are divisible by 4, so is the original number. 32 = 4 x 8 so as 32 is divisible by 4, so is 211032. An alternative test for 4: add the last digit to twice the preceding digit, and if this sum is divisible by 4 so is the original number. This can be repeated until a single digit remains which must be 4 or 8 (to be divisible by 4) if the original number is divisible by 4. for 211032: 2 + 3x2 = 8 → [single digit 8 which] is divisible by 4, so 211032 is also divisible by 4.
8888
1000.
2400
4000
No. To test if a number is divisible by 8: * first all multiples of 8 are even, so the number must be even; * then: add 4 times the hundreds digit to twice the tens digit to the ones digit - if this sum is divisible by 8, then so is the original number. As the test can be applied to the sum, repeating this summing until a single digit remains, only if this single digit is 8 is the original number divisible by 8. For 100: 4x1 + 2x0 + 0 = 4 which is not 8, so 100 is not divisible by 8.
10001000/8 = 125
4444
5040
2400
Yes. To check divisibility by 8 add the units digit to twice the ten's digit to four times the hundred's digit; if this sum is divisible by 8, so is the original number: 4 + 2x4 + 4x3 = 4 + 8 + 12 = 24 which is divisible by 8, so 110344 is also divisible by 8.