Question

Find the largest number which divides 378 and 510 leaving remainder 6 in each case.

Answer 1

We know that the required number divides 372 (378 − 6) and 504 (510 − 6).
∴ Required number = HCF (372, 504)
On applying Euclid's algorithm, we get:
372) 504 (1
−​ 372
132) 372 (2
−​ 264
108) 132 (1
−​ 108
24) 108 (4
−​ 96
12) 24 (2
−​ 24
0
Therefore, the HCF of 372 and 504 is 12.
Hence, the required largest number is 12.