Question

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

Answer 1

Largest number which divides 438 and 606, leaving remainder 6 is actually the largest number which divides 438 − 6 = 432 and 606 − 6 = 600, leaving remainder 0.

Therefore, HCF of 432 and 600 gives the largest number.

Now, prime factors of 432 and 600 are:
432 = 2⁴ × 3³
600 = 2³ × 3 × 5²

HCF = product of smallest power of each common prime factor in the numbers = 2³ × 3 = 24

Thus, the largest number which divides 438 and 606, leaving remainder 6 is 24.