Find the largest number which divides 438 and 606,

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:

$432=2^{4} \times 3^{3}$

$600=2^{3} \times 3 \times 5^{2}$

HCF = product of smallest power of each common prime factor in the numbers $=2^{3} \times 3=24$

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