Find the largest number which divides 438 and 606, leaving remainder 6 in each case.

Given: The number 438 and 606.

To find: The largest number which divides 438 and 606 and leaves remainder 6.

Concept Used:

Euclid's division lemma:

If there are two positive integers a and b,

then there exist unique integers q and r such that,

a = bq + r where 0 ≤ r ≤ b.

Explanation:

As the number leaves remainder 6,

So, if subtract 6 from each number the numbers will be completely divisible.

We have to find HCF of (438-6) and (606-6) that is 432 and 600.

Here 600 > 432

By Euclid’s division lemma

600 = 432× 1+168

As the remainder 168 ≠ 0

Apply the lemma in 432 and 168

⇒ 432 = 168× 2 + 96

As the remainder 96 ≠ 0

Apply the lemma in 168 and 96

⇒ 168 = 96 × 1 + 72

As the remainder 72 ≠ 0

Apply the lemma in 96 and 72

⇒ 96 = 72 × 1 + 24

As the remainder 24 ≠ 0

Apply the lemma in 72 and 24

⇒ 72 = 24 × 3 + 0

As remainder is 0 now,

So HCF is 24.

Hence the largest number is 24 which when divided by 438 and 606 leaves remainder 6.