# Is the integer number 768 divisible by 768?

## Latest divisibility operations

 Number 768 is divisible by 768. The two numbers are equal. Apr 07 17:28 UTC (GMT) Number 21 is not divisible by 4. Number 21 does not have (all) the prime factors of the number 4. Apr 07 17:28 UTC (GMT) Number 185 is divisible by 5. Number 185 has all the prime factors of the number 5. Apr 07 17:28 UTC (GMT) Number 6,435 is divisible by 9. Number 6,435 has all the prime factors of the number 9. Apr 07 17:28 UTC (GMT) Number 20 is divisible by 20. The two numbers are equal. Apr 07 17:28 UTC (GMT) Number 875 is not divisible by 243. Number 875 does not have (all) the prime factors of the number 243. Apr 07 17:28 UTC (GMT) Number 830 is divisible by 2. Number 830 has all the prime factors of the number 2. Apr 07 17:28 UTC (GMT) Number 12,772 is divisible by 6,386. Number 12,772 has all the prime factors of the number 6,386. Apr 07 17:28 UTC (GMT) Number 936 is divisible by 2. Number 936 has all the prime factors of the number 2. Apr 07 17:28 UTC (GMT) Number 6,435 is not divisible by 8. Number 6,435 does not have (all) the prime factors of the number 8. Apr 07 17:28 UTC (GMT) Number 1,155 is divisible by 3. Number 1,155 has all the prime factors of the number 3. Apr 07 17:28 UTC (GMT) Number 145 is not divisible by 3. Number 145 does not have (all) the prime factors of the number 3. Apr 07 17:28 UTC (GMT) Number 145 is not divisible by 3. Number 145 does not have (all) the prime factors of the number 3. Apr 07 17:28 UTC (GMT) integer numbers divisibility, see more...

## Divisibility of integer numbers

Let's divide two different numbers, 12 and 15, by 4. When we divide 12 by 4, the quotient is 3 and the operation leaves no remainder. But when we divide 15 by 4, the quotient is 3 and the operation leaves a remainder of 3. We say that the number 12 is divisible by 4 and 15 is not. We also say that 4 is a divisor of 12, but is not a divisor of 15.

## Some divisibility rules

The number 84 is divisible by 4 and 3 and is also divisible by 4 × 3 = 12. This is not true unless the two divisors are coprime.

#### In general, if "a" is divisible by both "m" and "n" and greatest common factor (m; n) = 1 (coprime numbers), then "a" it is also divisible by their product, (m × n).

Calculating divisors (factors) is very useful when simplifying fractions (reducing fractions to lower terms). The established rules for finding factors (divisors) are based on the fact that the numbers are written in the decimal system. Mutiples of 10 are divisible by 2 and 5, because 10 is divisible by 2 and 5; multiples of 100 are divisible by 4 and 25, because 100 is divisible by 4 and 25; multiples of 1000 are divisible by 8, because 1000 is divisible with 8. All the powers of 10, when divided by 3, or 9, have a remainder equal to 1.

Due to the rules of operation with remainders, we have the following remainders when dividing numbers by 3 or 9: 600 leaves a remainder equal to 6 = 1 × 6; 240 = 2 × 100 + 4 × 10, then the remainder will be equal to 2 × 1 + 4 × 1 = 6. On dividing a number by 3 or 9 the remainder will be equal to that left from dividing the sum of digits of that number by 3 or 9; 7,309 has the sum of the numbers 7 + 3 + 0 + 9 = 19, which is divided without a remainder to neither 3 nor 9. So 7,309 is not divisible by 3 or 9.

All even powers of 10, 100, 10,000, 1,000,000, etc., when divided by 11 left a remainder of 1, and the odd powers of 10, when divided by 11 left a remainder equal to 10 or 10 - 11 = -1. In this case, the alternating sum of the digits bears the same remainder as when dividing by 11, as if the whole number were being divided by 11. How to calculate the alternating sum is shown in the example below.

For instance, for the number: 85,976: 8 + 9 + 6 = 23, 5 + 7 = 12, the alternating sum of the digits: 23 - 12 = 11. So 85,976 is divisible by 11.

A number is divisible by:
• 2 if the last digit is divisible by 2
• 4 if the last two digits form a number divisible by 4;
• 8, if the last three digits form a number divisible by 8;
• 5 if the last digit is divisible by 5 (5 and 0)
• 25, if the last two digits form a number divisible by 25
• 3, if the sum of digits is divisible by 3;
• 9, if the sum of digits is divisible by 9;
• 11 if the alternating sum of digits is divisible by 11.