Question

find the greatest number that will divide 137,182and422 leaving the remainder 2in each case.​

Answer 1

Answer :

15

$\rule{100}2$

Solution :

It is given that,

• 137, 182 and 422 are divided by a greatest number that leaves remainder 2 in each case.

If it leaves remainder ' 2 ' in each case and we've to find the greatest number, then it means we've to find the H.C.F of :-

• 137-2 = 135
• 182-2 = 180
• 422-2 = 420

Now,

→ 135 = 3³ × 5

→ 180 = 2² × 3² × 5

→ 420 = 2² × 5 × 3 × 7

∴ H.C.F = 3 × 5

⇒ 15

Hence,

15 is the greatest number that will divide 137, 182 and 422 leaving remainder 2 in each case.

$\rule{200}2$