Question

find the largest number that will divide 398 , 436 and 542 leaving remainder s 7 , 11 , 15 respectively​

Answer 1

Step 1: Subtract the numbers.

$\sf 398-7-391\\\\ 436-11=425\\\\ 542-15=527$

Step 2: Find the HCF of the numbers obtained.

$\begin{array}{r | l} 17 & 391,425,527 \\ \cline{2-2} & 23,25,31 \\ \end{array}$

HCF of 391, 425 and 527 is 17

∴The answer is 17.

Additional Information

What is common factor?

When two or more numbers have the same factors, then these factors are known as common factors.

What is the Highest Common Factor (HCF)?

The highest common factor in the group of two or more numbers is known as the Highest Common Factor (HCF).

What are the methods to find the HCF of two or more numbers?

There are three methods to find HCF. They are ⇒

• HCF By Prime Factorization Method
• HCF By Division Method
• HCF by Shortcut method

Answer 2

$\mathfrak{\huge{\pink{\underline{Question:-}}}}$

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

$\mathfrak{\huge{\pink{\underline{Analysis:-}}}}$

We need to find the HCF of 3 numbers (398-7), (436-11) and (542-15). And the required number would be the HCF of the following numbers.

$\mathfrak{\huge{\pink{\underline{Solution:-}}}}$

$\sf 398-7=391$

$\sf 436-11=425$

$\sf 542-15=527$

Now, finding the HCF of 391, 425, 527

The factors of 391 are: 1, 17, 23, 391

The factors of 425 are: 1, 5, 17, 25, 85, 425

The factors of 527 are: 1, 17, 31, 527

Therefore, the HCF is 17

Hence, the largest number that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively is 17.

$\mathfrak{\huge{\pink{\underline{Points \; to \: Note:-}}}}$

The largest or greatest factor common to any two or more given natural numbers is termed as HCF of given numbers.

The highest common factor is found by multiplying all the factors which appear in both lists.

HCF of any two or more numbers is never greater than any of the given numbers.