Answer :

To solve the problem of finding the Highest Common Factor (H.C.F.), also known as the Greatest Common Divisor (G.C.D.), we need to evaluate the numbers given.

First, let's address the claim that the H.C.F. of (120, 504, 882) is 6.47. The H.C.F. should always be a whole number because it represents the largest integer by which each of the numbers can be divided without leaving a remainder. Therefore, 6.47 cannot be the H.C.F. for any set of numbers.

To find the correct H.C.F. of the numbers 120, 504, and 882, we can use the prime factorization method:

  1. Prime Factorization

    • 120 = 2^3 \times 3^1 \times 5^1
    • 504 = 2^3 \times 3^2 \times 7^1
    • 882 = 2^1 \times 3^2 \times 7^1 \times 11^1

  2. Identify the Common Prime Factors

    • The only common prime factor is 2^1 and 3^1.

  3. Find the H.C.F

    • H.C.F = 2^1 \times 3^1 = 6

Thus, the correct H.C.F. of 120, 504, and 882 is 6.

Next, consider the statement about the H.C.F. of 15 and 51. When finding the H.C.F., we identify the largest number that divides both numbers without a remainder:

  • 15 = 3 \times 5
  • 51 = 3 \times 17

The H.C.F. is 3, since 3 is the largest number that can divide both 15 and 51. This means that the statement "The H.C.F. of 15 and 51 is not 1" is correct as their H.C.F is indeed 3.

In summary:

  • The H.C.F. of (120, 504, 882) is 6.
  • The H.C.F. of 15 and 51 is 3.

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