# Find the largest number that will divide 398 , 436 and 542 leaving remainders 7 , 11 and 15 respectively

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The largest number that will divide 398, 436, and 542 leaving remainders 7, 11, and 15 respectively is 17. The greatest number that will divide 398, 436, and 542 and leave the corresponding remainders of 7, 11, and 15 can be found by using a few simple steps. We can determine the largest number required by taking the HCF of three numbers that are 398-7, 436-11, and (542-15).

## Largest Number that will Divide 398, 436, 542 Leaving Remainders 7, 11, 15

To know the solution to the problem of finding the largest number that will divide 398, 436, and 542 leaving remainders 7, 11, and 15, we will first divide the numbers by their reminders.

Hence,

436 – 11 = 425

398 – 7 = 391

542 – 15 = 527

Next, we will calculate the HCF of these new numbers. This will be the largest possible number that can divide 391, 425, and 527 while leaving the remainder we need.

Now, as we can see the HCF of these numbers (391, 425, 527) = 17

Therefore, 17 is the highest number that will divide 398,436 and 542, leaving 7, 11, and 15 as the remainder.

## Numbers

A number is an arithmetic value used to calculate and represent a quantity. Numerical symbols, such as 3, are written to represent numbers. A number system is a logical way of writing numbers that use digits or symbols to represent them. the system of numbers

• represents a practical collection of numbers.
• reflects a number’s arithmetic and algebraic structure.
• Standard representation is offered.

## Number Series

In mathematics, a number series is a set of numbers where each term is a different number, and the following term is formed by either adding or subtracting the last term from the previous term. Consider the series 1, 3, 5, 7, and 9, for instance. The constant term 2 is added to the preceding term in this series to produce the subsequent term.

Summary

## Find the largest number that will divide 398, 436, and 542 leaving remainders 7, 11, and 15 respectively

The biggest number that will divide 398, 436, and 542 with 7, 11, and 15 as the remaining fractions are 17. We reached this solution by first subtracting the remainder from their respective numbers. after that, by using these new numbers we calculated the HCF which gave us our answer.

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