# Find the Largest Number Which Divides 615 and 963 Leaves the Remainder 6 in Each

By BYJU'S Exam Prep

Updated on: September 25th, 2023

87 is the largest number which divides 615 and 963 leaves the remainder 6 in each. To derive this answer, we will first take into consideration the numbers given and the remainder. We will then subtract remainder from these numbers. We will have a new set of numbers who see HCF will provide us with the largest number that can divide 615 and 963 while leaving 6 as a remainder in each.

## Largest Number Which Divides 615 and 963 Leaves the Remainder 6

To find the largest number which divides 615 and 963 and leaves the remainder 6 in each, we will first find subtract the remainder from these numbers. As we will subtract 6 from 615 and 963, it will leave us with this –

615 – 6 = 609

963 – 6 = 957

Now, we will solve the rest of the question by finding the HCF using prime factorization method for the given set of numbers that we have just derived.

Let x be the required largest number

609 = 29 x 3 x 7

957 = 29 x 11 x 3

The common factors are 29 and 3

x = 29 x 3

x = 87

Thus, the largest number which divides 615 and 963 leaves the remainder 6 in each is 87.

## HCF – Highest Common Factor

The abbreviation for this phrase is Highest Common Factor. The HCF of two numbers is the highest factor that may divide two integers equally. It is possible to evaluate HCF using two or more numbers. It is the most effective divisor for any pair of integers that may evenly or completely divide the inputted numbers.

## HCF by Prime Factorization Method

The methods below will show you how to calculate a number’s HCF using prime factorization.

Step 1: Summarize each integer’s prime factors for each integer. This approach is known as prime factorization.

Step 2: List the components that both numbers share in step two.

The HCF is the total of all the common prime factors in step three (use the lower power of each common factor)

Summary:

## Find the Largest Number Which Divides 615 and 963 Leaves the Remainder 6 in Each

87 is the largest number which divides 615 and 963 leaves the remainder 6 in each. HCF of two numbers is the highest factor which divides the two numbers, evenly. It can be found for two or more than two numbers.

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