Find the HCF 240,330,339

Mathematics

ScanSolve AI Answer

Answer

3

Step-by-step solution

4 steps

  1. Find the prime factorization of each number.

    For 240:

    240=24×10=(23×3)×(2×5)=24×31×51240 = 24 \times 10 = (2^3 \times 3) \times (2 \times 5) = 2^4 \times 3^1 \times 5^1

    For 330:

    330=33×10=(3×11)×(2×5)=21×31×51×111330 = 33 \times 10 = (3 \times 11) \times (2 \times 5) = 2^1 \times 3^1 \times 5^1 \times 11^1

    For 339:

    339=3×113339 = 3 \times 113

    (Note: 113 is a prime number.)

  2. Identify the common prime factors among all three numbers.

    • The prime factors of 240 are $2, 3, 5$.
    • The prime factors of 330 are $2, 3, 5, 11$.
    • The prime factors of 339 are $3, 113$. The only prime factor common to all three numbers is 3.

  3. Identify the lowest power of the common prime factor.

    For the common prime factor 3:

    • In 240, the power is 313^1.
    • In 330, the power is 313^1.
    • In 339, the power is 313^1. The lowest power of 3 is 313^1.

  4. Multiply the lowest powers of the common prime factors to find the HCF.

    HCF(240,330,339)=31=3\text{HCF}(240, 330, 339) = 3^1 = 3

    The HCF of 240,330,240, 330, and 339 is 3\boxed{3}.

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