Find the H.C.F of 9,15, and 24

Mathematics

ScanSolve AI Answer

Answer

3

Step-by-step solution

4 steps

The H.C.F. of 9, 15, and 24 is 3.

  1. Prime Factorization of Each Number

    Find the prime factors for each given number.

    9=3×3=329 = 3 \times 3 = 3^2 15=3×515 = 3 \times 5 24=2×2×2×3=23×324 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3

  2. Identify Common Prime Factors

    Identify the prime factors that are common to all three numbers.
    The only common prime factor is 3.

  3. Determine the Lowest Power of Common Prime Factors

    For each common prime factor, take the lowest power it appears in any of the factorizations.
    For the prime factor 3, the powers are 323^2 (from 9), 313^1 (from 15), and 313^1 (from 24). The lowest power is 313^1.

  4. Calculate the H.C.F.

    Multiply the common prime factors raised to their lowest powers.

    H.C.F.=31=3\text{H.C.F.} = 3^1 = 3

    The H.C.F. of 9, 15, and 24 is 3\boxed{3}.

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