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22 November, 03:19

100pts: Explain the how to use the Euclidean algorithm for finding the GCF of 675 and 150

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  1. 22 November, 03:32
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    Greatest (highest) common factor (divisor)

    gcf, hcf, gcd (675; 150) = 75 = 3 * 52;

    The numbers have common prime factors.

    Step-by-step explanation:

    675 = 33 * 52;

    150 = 2 * 3 * 52;

    Multiply all the common prime factors, by the lowest exponents.

    Greatest (highest) common factor (divisor):

    gcf, hcf, gcd (675; 150) = 3 * 52

    Step 1. Divide the larger number by the smaller one:

    675 : 150 = 4 + 75;

    Step 2. Divide the smaller number by the above operation's remainder:

    150 : 75 = 2 + 0;

    At this step, the remainder is zero, so we stop:

    75 is the number we were looking for, the last remainder that is not zero.

    This is the greatest common factor (divisor).

    Greatest (highest) common factor (divisor):

    gcf, hcf, gcd (675; 150) = 75

    gcf, hcf, gcd (675; 150) = 75 = 3 * 52
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