Find the H. C. F of 18,24,and 32

Mathematics

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Step-by-step solution

5 steps

The H.C.F. of 18, 24, and 32 is 2.

  1. Find the prime factorization of 18

    18=2×3×3=21×3218 = 2 \times 3 \times 3 = 2^1 \times 3^2

  2. Find the prime factorization of 24

    24=2×2×2×3=23×3124 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3^1

  3. Find the prime factorization of 32

    32=2×2×2×2×2=2532 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5

  4. Identify common prime factors and their lowest powers

    The common prime factor among 18, 24, and 32 is 2.
    The lowest power of 2 present in the factorizations is 212^1 (from 18).
    The prime factor 3 is not common to all three numbers (it's missing in 32).

  5. Calculate the H.C.F.

    Multiply the common prime factors raised to their lowest powers.

    H.C.F.=21=2\text{H.C.F.} = 2^1 = 2

    The H.C.F. of 18, 24, and 32 is 2\boxed{2}.

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