# What will be the Greatest Number? If

The greatest number by which 2300 and 3500 are divided leaving the remainders of 32 and 56 respectively, is:

- 136
- 168
- 42
- 84

**Answer: (4) 84
Explanation:-**

Numbers are = 2300 and 3500

Remainders = 32 and 56

New numbers = 2300 – 32 = 2268 and 3500 – 56 = 3444

The HCF of 2268 and 3444

Factors of 2268 = 2 x 2 x 3 x 3 x 3 x 3 x 7

Factors of 3444 = 2 x 2 x 3 x 7 x 41

HCF = 2 x 2 x 3 x 7 = 84

Hence, the answer is (4) 84.