Divisible by 8 and by 9
- Input
- 7128
- Expected output
- 128 ÷ 8 = 16 e 7 + 1 + 2 + 8 = 18
7,128 = 8 × 891; it is also divisible by 2, 3, 4, 6 and 11.
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divisibility rules
The divisibility rules tell you whether a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10 or 11 by looking only at its digits, with no division. The Divisibility tab of the calculator shows each rule with the value read from your number and confirms the result with the actual division.
7,128 = 8 × 891; it is also divisible by 2, 3, 4, 6 and 11.
Even with sum 21 (a multiple of 3), so divisible by 6; the sum is not a multiple of 9.
The last two digits, 25, do not form a multiple of 4.
-22 is a multiple of 11, and the quotient is 83,462.
A sum of 0 counts as a multiple of 11: 1,001 = 11 × 91.
There are two ways. The direct one is to test the whole numbers from 1 up to the square root of the number: each time the division is exact you gain two divisors, the tested one and the quotient. For 36, testing 1, 2, 3, 4, 5 and 6 gives the pairs (1, 36), (2, 18), (3, 12), (4, 9) and (6, 6). Factoring is faster for large numbers: break the number into primes and combine the powers, which is what the Step by step tab shows.
Add the digits. If the result is a multiple of 3, so is the number. If the sum is still large, add again: 8,742 gives 21, then 3.
When it is divisible by both 3 and 4, since 3 and 4 share no divisor other than 1. The same reasoning works for 6 (2 and 3) and for 15 (3 and 5).
Yes. If 4 divides the number, 2 does too, since 4 = 2 × 2. The reverse does not hold: 6 is divisible by 2 but not by 4.
Because every power of 10 leaves remainder 1 when divided by 9 (10 = 9 + 1, 100 = 99 + 1). So a number 345 = 3 × 100 + 4 × 10 + 5 leaves the same remainder as 3 + 4 + 5 = 12, that is, remainder 3.
36 has 9 divisors
The proper divisors add up to 55, which is 19 more than 36: an abundant number.
Divisors that are prime are highlighted.
Accepts whole numbers of up to 18 digits. Everything runs in your browser with exact arithmetic.
Related: GCD and LCM · Prime numbers · Simplify fractions