Divisibility by 7 or 13

What is divisibility?

The division is considered to be one of the common yet complex topics and functions in the field of mathematics.

The potential to be divided by a number is the divisibility of a given number. In simple words a number is divisible by another number to give a remainder of zero when they are divided is called the divisibility of a number.

Divisibility rules are a set of general policies and terms that one must follow and obey to find if a number is fully divisible by another number. There are several rules such as divisibility by 7, divisibility by 13, etc…

Some Divisibility Rules Are As Follows

Divisibility Rule Of Number 7

The last digit of a given whole number is doubled (twice) and is then subtracted from the remaining number. If this difference is divisible by 7 then the original number as a whole is also divisible by 7.

Example-

336

Double the last number = 6 x 2 = 12

Subtract it from the remaining number = 33 – 12 = 21

The result is 21 which is divisible by 7 thus the original number 336 is also divisible by 7.

336 ÷ 7 = 48.

553

Double the last number = 3 x 2 = 6

Subtract it from the remaining number = 55 – 6 = 49

The result is 49 which is divisible by 7 thus the original number 553 is also divisible by 7.

553 ÷ 7 = 79.

847

Double the last number = 7 x 2 = 14

Subtract it from the remaining number = 84 – 14 = 70

The result is 70 which is divisible by 7 thus the original number 847 is also divisible by 7.

847 ÷ 7 = 121.

Divisibility Rule Of Number 13

The  rule for divisibility of 13 says that if a number can be divisible by 13 if the digit in the one’s place is multiplied by 4 and the product is added to the remainder of the number, which either yields 0 or a multiple of 13. In other words, the addition of multiplication of the units digit by 4 and the remaining number with itself must be a zero or it should not give any residual number apart from zero when divided by 13.

For example an individual must take the last two digits of a given number and minus it from the multiplication of 4 and the remaining number. If the resulting number is a multiple of 13 or zero, then we say that the number is divisible by the number 13. 

If the given number is 650, then the last two digits are 50. Multiplication of 4 and the rest of the number, that is 4 x 6 = 24, that is 24. On subtracting the last two numbers and the result of the subtraction being: 50 – 24 = 26, we get 26. The number 26 is a divisor of 13. Thus, 650 is divisible by 13. This way of divisibility of the number 13 can be easily applied and very effective for three-digit numbers also.

Other method to find the divisibility of Number 13-

Is Number 298 divisible by 13?

Last digit multiplied by 4 = 8 x 4 = 32

Remaining Digit = 29

Add the Remaining Digit and the result of the Last two digits multiplied by 4 = 29 + 32

= 61 is not divisible by 13 hence 298 is not a divisible by 13.

Is Number 247 divisible by 13?

Last digit multiplied by 4 = 7 x 4 = 28

Remaining Digit = 24

Add the Remaining Digit and the result of the Last two digits multiplied by 4 = 24 + 28

= 52 is divisible by 13 hence 247 is divisible by 13.

Conclusion

Divisibility helps a student to get his mathematical solutions quicker. Knowing the rules of divisibility can help one find the divisible and divide greater numbers just with the help of his/her fingertips.