Question

Find the greatest number that will divide 445, 572 and 699, leaving remainders 4, 5, 6 respectively.

Answer 1

Since the respective remainders of 445, 572, and 699 are 4, 5, and 6, we have to find the number which exactly divides (445-4), (572-5), and (696-6).
So, the required number is the HCF of 441, 567, and 693.
Firstly, we will find the HCF of 441 and 567.

∴ HCF = 63
Now, we will find the HCF of 63 and 693.

∴ HCF = 63
Hence, the required number is 63.