Answer :

To find the Highest Common Factor (HCF) of given numbers, we need to determine the largest number that can divide each of the numbers without leaving a remainder.

Let's break it down step-by-step for each part of the question:

a) H.C.F of 21 and 42:

  1. List Factors:

    • Factors of 21: [tex]1, 3, 7, 21[/tex]
    • Factors of 42: [tex]1, 2, 3, 6, 7, 14, 21, 42[/tex]

  2. Common Factors: Both 21 and 42 have common factors [tex]1, 3, 7,[/tex] and [tex]21[/tex].

  3. Highest Common Factor: The largest common factor is [tex]21[/tex].

b) H.C.F of 27 and 36:

  1. List Factors:

    • Factors of 27: [tex]1, 3, 9, 27[/tex]
    • Factors of 36: [tex]1, 2, 3, 4, 6, 9, 12, 18, 36[/tex]

  2. Common Factors: Both 27 and 36 have common factors [tex]1, 3, 9[/tex].

  3. Highest Common Factor: The largest common factor is [tex]9[/tex].

c) H.C.F of 24, 36, and 48:

  1. List Factors:

    • Factors of 24: [tex]1, 2, 3, 4, 6, 8, 12, 24[/tex]
    • Factors of 36: [tex]1, 2, 3, 4, 6, 9, 12, 18, 36[/tex]
    • Factors of 48: [tex]1, 2, 3, 4, 6, 8, 12, 16, 24, 48[/tex]

  2. Common Factors: All three numbers share common factors [tex]1, 2, 3, 4, 6, 12[/tex].

  3. Highest Common Factor: The largest common factor is [tex]12[/tex].

So, the HCFs are:

  • For 21 and 42, it's 21.
  • For 27 and 36, it's 9.
  • For 24, 36, and 48, it's 12.

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