Divisibility criteria

Divisibility Rules (Byjus)

Reference

Byjus. (2023, March 20). [i]Divisibility rules from 1 to 13: Division rules in Maths[/i]. BYJUS. https://byjus.com/maths/divisibility-rules/ [br]

Quiz

Answer the following questions to reinforce what you just learnt in the previous reference.

Divisibility by 2

Choose the right option:[br][b]An integer number is divisible by [math]2[/math] if:[/b]

The difference between the sum of the digits in even position and the sum of the digits in odd position is 0 or a multiple of 11. Its last digit is 0 or 5. Its last three digits form a multiple number of 8. If the difference between the number formed by all the digits except the units digit and nine times the units digit, is 0 or a multiple of 13. The sum of its digits is a multiple of 9. If the difference between the number formed by all the digits except the units digit and twice the units digit, is 0 or a multiple of 7. Its last digit is 0, 2, 4, 6, or 8. Its last digit is 0, 2, 4, 6, or 8 and the sum of its digits is a multiple of 3. Its last two digits form a multiple number of 4. The sum of its digits is a multiple of 3.

Divisibility by 3

Choose the right option:[br][b]An integer number is divisible by [math]3[/math] if:[/b]

Its last three digits form a multiple number of 8. The difference between the sum of the digits in even position and the sum of the digits in odd position is 0 or a multiple of 11. If the difference between the number formed by all the digits except the units digit and twice the units digit, is 0 or a multiple of 7. Its last two digits form a multiple number of 4. Its last digit is 0, 2, 4, 6, or 8. The sum of its digits is a multiple of 9. Its last digit is 0, 2, 4, 6, or 8 and the sum of its digits is a multiple of 3. If the difference between the number formed by all the digits except the units digit and nine times the units digit, is 0 or a multiple of 13. Its last digit is 0 or 5. The sum of its digits is a multiple of 3.

Divisibility by 4

Choose the right option:[br][b]An integer number is divisible by [math]4[/math] if:[/b]

The sum of its digits is a multiple of 3. Its last digit is 0, 2, 4, 6, or 8. Its last digit is 0, 2, 4, 6, or 8 and the sum of its digits is a multiple of 3. If the difference between the number formed by all the digits except the units digit and nine times the units digit, is 0 or a multiple of 13. The sum of its digits is a multiple of 9. Its last digit is 0 or 5. The difference between the sum of the digits in even position and the sum of the digits in odd position is 0 or a multiple of 11. If the difference between the number formed by all the digits except the units digit and twice the units digit, is 0 or a multiple of 7. Its last three digits form a multiple number of 8. Its last two digits form a multiple number of 4.

Divisibility by 5

Choose the right option:[br][b]An integer number is divisible by [math]5[/math] if:[/b]

Its last three digits form a multiple number of 8. Its last digit is 0, 2, 4, 6, or 8. The difference between the sum of the digits in even position and the sum of the digits in odd position is 0 or a multiple of 11. Its last digit is 0 or 5. Its last two digits form a multiple number of 4. Its last digit is 0, 2, 4, 6, or 8 and the sum of its digits is a multiple of 3. If the difference between the number formed by all the digits except the units digit and nine times the units digit, is 0 or a multiple of 13. The sum of its digits is a multiple of 3. If the difference between the number formed by all the digits except the units digit and twice the units digit, is 0 or a multiple of 7. The sum of its digits is a multiple of 9.

Divisibility by 6

Choose the right option:[br][b]An integer number is divisible by [math]6[/math] if:[/b]

If the difference between the number formed by all the digits except the units digit and nine times the units digit, is 0 or a multiple of 13. Its last digit is 0, 2, 4, 6, or 8. Its last three digits form a multiple number of 8. If the difference between the number formed by all the digits except the units digit and twice the units digit, is 0 or a multiple of 7. Its last digit is 0, 2, 4, 6, or 8 and the sum of its digits is a multiple of 3. The difference between the sum of the digits in even position and the sum of the digits in odd position is 0 or a multiple of 11. Its last two digits form a multiple number of 4. Its last digit is 0 or 5. The sum of its digits is a multiple of 3. The sum of its digits is a multiple of 9.

Divisibility by 7

Choose the right option:[br][b]An integer number is divisible by [math]7[/math] if:[/b]

If the difference between the number formed by all the digits except the units digit and nine times the units digit, is 0 or a multiple of 13. Its last digit is 0, 2, 4, 6, or 8 and the sum of its digits is a multiple of 3. Its last two digits form a multiple number of 4. Its last digit is 0, 2, 4, 6, or 8. The sum of its digits is a multiple of 3. The sum of its digits is a multiple of 9. Its last digit is 0 or 5. The difference between the sum of the digits in even position and the sum of the digits in odd position is 0 or a multiple of 11. If the difference between the number formed by all the digits except the units digit and twice the units digit, is 0 or a multiple of 7. Its last three digits form a multiple number of 8.

Divisibility by 8

Choose the right option:[br][b]An integer number is divisible by [math]8[/math] if:[/b]

Its last two digits form a multiple number of 4. Its last digit is 0, 2, 4, 6, or 8. The difference between the sum of the digits in even position and the sum of the digits in odd position is 0 or a multiple of 11. Its last digit is 0, 2, 4, 6, or 8 and the sum of its digits is a multiple of 3. If the difference between the number formed by all the digits except the units digit and twice the units digit, is 0 or a multiple of 7. If the difference between the number formed by all the digits except the units digit and nine times the units digit, is 0 or a multiple of 13. The sum of its digits is a multiple of 3. Its last three digits form a multiple number of 8. Its last digit is 0 or 5. The sum of its digits is a multiple of 9.

Divisibility by 9

Choose the right option:[br][b]An integer number is divisible by [math]9[/math] if:[/b]

The sum of its digits is a multiple of 9. Its last digit is 0, 2, 4, 6, or 8 and the sum of its digits is a multiple of 3. The sum of its digits is a multiple of 3. Its last digit is 0 or 5. If the difference between the number formed by all the digits except the units digit and twice the units digit, is 0 or a multiple of 7. Its last digit is 0, 2, 4, 6, or 8. The difference between the sum of the digits in even position and the sum of the digits in odd position is 0 or a multiple of 11. Its last three digits form a multiple number of 8. Its last two digits form a multiple number of 4. If the difference between the number formed by all the digits except the units digit and nine times the units digit, is 0 or a multiple of 13.

Divisibility by 11

Choose the right option:[br][b]An integer number is divisible by [math]11[/math] if:[/b]

Its last digit is 0, 2, 4, 6, or 8. Its last digit is 0 or 5. If the difference between the number formed by all the digits except the units digit and nine times the units digit, is 0 or a multiple of 13. The sum of its digits is a multiple of 3. Its last digit is 0, 2, 4, 6, or 8 and the sum of its digits is a multiple of 3. The difference between the sum of the digits in even position and the sum of the digits in odd position is 0 or a multiple of 11. If the difference between the number formed by all the digits except the units digit and twice the units digit, is 0 or a multiple of 7. Its last two digits form a multiple number of 4. The sum of its digits is a multiple of 9. Its last three digits form a multiple number of 8.

Divisibility by 13

Choose the right option:[br][b]An integer number is divisible by [math]13[/math] if:[/b]

The sum of its digits is a multiple of 3. Its last digit is 0 or 5. Its last digit is 0, 2, 4, 6, or 8 and the sum of its digits is a multiple of 3. Its last two digits form a multiple number of 4. If the difference between the number formed by all the digits except the units digit and nine times the units digit, is 0 or a multiple of 13. Its last three digits form a multiple number of 8. The sum of its digits is a multiple of 9. If the difference between the number formed by all the digits except the units digit and twice the units digit, is 0 or a multiple of 7. Its last digit is 0, 2, 4, 6, or 8. The difference between the sum of the digits in even position and the sum of the digits in odd position is 0 or a multiple of 11.