Determine the greatest number by which 420, 458, and 569 should be divided, resulting in remainders of 6, 8, and 11 respectively?

**A.**18**B.**21**C.**17**D.**24

Answer: **A.** 18

**Given:** 420, 458, and 569 are three numbers leaving the remainder 6, 8, and 11 on dividing with the greatest number

- 420 − 6 = 414
- 458 − 8 = 450
- 569 − 11 = 558

Now, let’s find the HCF(414,450,558)

To find the highest common factor (HCF) of 414, 450, and 558, we can use the prime factorization method.

- Find the prime factorization of each number:
- 414 = 2×3×3×23
- 450 = 2×3×3×5×5
- 558 = 2×3×7×11

- Identify the common prime factors and their lowest powers:
- Common factors: 2×3×3=18

So, the HCF of 414, 450, and 558 is **18**.