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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.

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

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 --&gt; 3 * 3
12--&gt; 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)

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