Question

What is the greatest number by which when 653, 869 and 1229 divided leave the same remainder?

1. 69
2. 78
3. 56
4. 72

Answer 1

Correct Answer - Option 4 : 72

Given:

The given numbers are 653, 869 and 1229

Concept Used:

HCF (Highest Common Factor): HCF of x and y is the highest common factor which can divide x and y exactly

For Example,

12 → Factors of 12 are 1, 2, 3, 4, 6 and 12

16 → Factors of 16 are 1, 2, 4, 8 and 16

Here common factors are 1, 2 and 4. But of these 4 is the largest/highest

∴ HCF of 12 and 16 is 4

⋆ HCF of two or more number will be their difference or a factor of their difference

Calculation:

Here,

869 – 653 = 216

1229 – 869 = 360

1229 – 653 = 576

HCF of 216, 360 and 576 is 72

∴ the required greatest number is 72