Vedic math trick: Calculation of remainder on division by 9

Remainder on division by 9

In Vedic mathematics, there is a simple rule to compute the remainder when a number is divided by 9. This rule is based on the fact that the sum of the digits of a number is congruent to the remainder of the division by 9.

Here's how it works:

Take the number you want to divide by 9.

Add up all its digits.

Find the remainder when the sum of the digits is divided by 9.

The remainder obtained in step 3 will be the same as the remainder when the original number is divided by 9.

Let's take an example to illustrate this:

Suppose you want to find the remainder when 4572 is divided by 9.

The number is 4572.

Sum of its digits: 4 + 5 + 7 + 2 = 18.

Divide the sum by 9: 18 ÷ 9 = 2 with a remainder of 0.

Therefore, the remainder when 4572 is divided by 9 is 0.

Let's take another example:Suppose you want to find the remainder when 8935 is divided by 9.

The number is 8935.Sum of its digits: 8 + 9 + 3 + 5 = 25.

Divide the sum by 9: 25 ÷ 9 = 2 with a remainder of 7.

Therefore, the remainder when 8935 is divided by 9 is 7.

This rule simplifies the process of finding remainders when dividing by 9 and is based on the concept of divisibility rules and modular arithmetic.

Learn More :

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