Question

Find the largest integer which divides 930 and 2317 leaving remainders 6 and 7 respectively.

Answer 1

462 is the largest integer which divides 930 and 2317 leaving remainders 6 and 7 respectively.

Given:

• Number divides 930 and 2317 leaving remainders 6 and 7 respectively

To Find:

• Largest Integer

Solution:

Step 1:

Assume that largest integer is k

then   930 = Ak  + 6   => Ak = 924

and  2317 = Bk  + 7  => Bk = 2310

Hence k is the HCF of 924 and 2310

Step 2:

Find HCF pf 924 and 2310

2310 = 924 x 2  + 462

924 = 462 x 2

Hence 462 is the HCF

462 is the largest integer which divides 930 and 2317 leaving remainders 6 and 7 respectively.