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    Working with Prime factorization

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    Rewrite in the simplest form. State the GCF(greatest common factor) of numerator and denominator in each case.

    1. 34/85

    2. 123123/567567

    Find 5/9+7/12 using three different denominators. Give your answers as mixed numbers in lowest terms. State the LCM (least common multiple)of the denominators.

    © BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddf
    https://brainmass.com/math/number-theory/working-prime-factorization-14001

    SOLUTION This solution is FREE courtesy of BrainMass!

    The Greatest Common Factor is the largest number that is a common factor of two or more numbers.

    To find the greatest common factor:

    Make a list of factors for each whole number.
    Identify the factors that are common to all lists.
    The greatest common factor is the largest of these common factors

    Q1. 34/85 = 17*2/17*5

    GCF is 17 ---(Answer)

    Also, 34/85 = 2/5 ---(Answer)

    Q2. 123123/567567

    = 3*41041/(3*3*3*21021)

    = 3*41041/(3*3*3*3*7*1001)

    = 3*7*5863/(3*3*3*3*7*1001)

    = 3*7*11*533/(3*3*3*3*7*11*91)

    = 3*7*11*13*41/(3*3*3*3*7*11*7*13)

    Now following the above steps, we get GCF = 13 ---(Answer)

    Also, 123123/567567 = 41/(3*3*3*7) = 41/189 ---(Answer)

    To find LCM, write down the numbers factorised

    9 --> 3 * 3
    12--> 4 * 3

    Now, LCM = 3 * 4 * 3 = 36 ---(Answer)

    1. Multiply by LCM and divide throughout by LCM

    {36*(5/9) + 36*(7/12)/36 = [20+21]/36 = 41/36

    = 1 (5/36) Mixed form ---Ans

    (36*1 + 5 = 41, the numerator)

    2.Now take the product of 9 and 12 = 108

    {108*(5/9) + 108*(7/12)/108 = [60+63]/108 = 123/108 = 1 (15/108)--Ans

    3. Now take 72 as the denomenator

    {72*(5/9) + 72*(7/12)/108 = [40+42]/72 = 82/72

    = 1 (10/72) ---Ans

    = 1 (5/36)

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddf>
    https://brainmass.com/math/number-theory/working-prime-factorization-14001

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