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

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.

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