What will be obtained if 8 is subtracted from the H.C.F. of 168, 189 and 231 ?

To find the final result, we need to first calculate the Highest Common Factor (H.C.F.) of 168, 189, and 231, and then subtract 8 from that value.

Step-by-Step Calculation

1. Find the H.C.F. of 168, 189, and 231: We can find the H.C.F. by prime factorization or by finding the differences between the numbers.

• Prime Factorization:

  • 168 = 2 × 84 = 2² × 42 = 2³ × 21 = 2³ × 3 × 7

  • 189 = 3 × 63 = 3² × 21 = 3³ × 7

  • 231 = 3 × 77 = 3 × 7 × 11

• Identify Common Factors:

  • The only prime factor common to all three numbers (168, 189, and 231) is 3 and 7.

  • H.C.F. = 3 × 7 = 21.

2. Subtract 8 from the H.C.F.:

• H.C.F. = 21

• Result = 21 - 8 = 13.