# Find the largest number which divides 70 and 125 leaves remainders 5 and 8 respectively.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

13 is the largest number which divides 70 and 125 leaves remainders 5 and 8 respectively. The solution to this problem can be derived by taking into consideration the fact that one has to divide the numbers with their remainders and then find the HCF. HCF will give the highest common factor between these numbers that provide the required remainders.

## Largest Number Divided by 70 and 125 Leaving Remainders 5 and 8

To find the largest number divisible by 70 and 125 which leaves the remainder 5 and 8 respectively. We will first subtract these numbers from their respective remainders. Thus, we will derive the following numbers –

70−5 = 65

125−8 = 117

Now, that we have these newly derived numbers after subtracting the original numbers from their remainder, we will find the HCF for them.

65=5×13

117=3×3×13

HCF (65, 117) = 13

Hence, 13 is the required largest number that divides 70 and 125 in a way that it leaves the remainder 5 and 8 respectively.

## What is a Remainder?

The remainder is an essential part of division problems in mathematics. It is the leftover number after two numbers have been divided. The remainder of two numbers is zero when two numbers are divisible from each other completely. However, if two numbers are completely divisible from each other, then the remainder is greater than 0. The value of a divisor is always greater than that of a remainder.

Summary:

## Find the largest number which divides 70 and 125 leaves remainders 5 and 8 respectively.

The largest number which divides 70 and 125 leaves remainders 5 and 8 respectively is 13. The highest common factor between 70 and 125 after subtraction of remainders helped provide this answer.

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