## Divisibility Rules for Prime Numbers Prime numbers between 10 and 20 are subject to intermediate divisibility laws.

The criteria for primes 2, 3, 5, 7, and 11 have already been covered.

See below for the rules for dividing by 13, 17, and 19.

## Divisibility Rule of 13

When divided by 13, the result is zero or less than that integer. Hence that number is divisible by 13.

The 13-test for divisibility allows us to determine whether a given number is divisible by 13 without resorting to time-consuming lengthy division.

First, we multiply the digit in the one’s place by 4 because that’s what the rule of 13 requires.

The digit to the left of the unit’s position is subtracted from the remainder before adding the product.

A number is divisible by 13 if the sum of its digits is divisible by 13.

## Divisibility Rule of 17

If there is no residual when dividing a number by 17, then that number is divisible by 17.

By applying the 17-rule of divisibility, we first increase the ones place digit by 5.

After that, the remainder of the number to its left (without the unit’s place digit) is subtracted from the product.

When a difference is subtracted from a number, if the resulting number is divisible by 17, then the original number is divisible by 17.

## Divisibility Rule of 19

To be divisible by 19, a number must result in a remainder of zero when divided by 19.

First, we must multiply the digit in the one’s place by 2 because that’s what the divisibility rule for 19 says has to happen.

The digit to the left of the unit’s position is subtracted from the remainder before adding the product.

If the result is a number divisible by 19, then the original number is divisible by 19.

### Complex Divisibility Checking Questions

• A given integer divides evenly by both 4 and 12. Will it really have a divisor of 48?
• See if the number 2359334 can be divided by both 4 and 8 easily.

## Rule of Divisibility: Some Hints and Tips

• When verifying prime numbers, it’s crucial to adhere to the norms of divisibility.
• Useful for working out word difficulties.
• In a nutshell, they can be used for rapid math.
• Every even number can be split in half exactly twice.
• One may always count on a leap year to be divisible by 4. News