What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?

∵ we are getting 5 as remainder.

Subtracting 5 from the dividend will give us the exact division.

So let’s subtract the remainder and find the HCF of numbers (largest number which divides both the number) -

We need to find HCF of 245 - 5 = 240 and 1029 - 5 = 1024.

Prime factorization of numbers -

240 = 2 × 2 × 2 × 2 × 3 × 5

1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

HCF of given numbers = 2 × 2 × 2 × 2 = 16.