How to Find the Greatest Common Factor (GCF)
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Whenever we multiply two whole numbers, we get another number. Now, basically, the numbers we multiplied to get the product, are called the factors of the product. So, for example, 2×3=62×3=6, this implies that 22 and 33 are the factors of 66. Another conclusion which we can draw from this is, that factors of a number completely divide the number without leaving any remainder.
For ex: Let’s consider the number 2424. Now 2424 can be divided into factors 66 and 44. Also 66 can be further factorized into 33 and 22. Moreover, 44 can also be factorized into 22 and 22. So, from this we can see that the other factors of 2424 are 33, 88 and 22. This is because 12×2=8×3=3×8=2412×2=8×3=3×8=24. Now, let’s learn some facts about factors.
- Each and every number has a smallest factor which is 11.
- Every number has a minimum of two factors that is 11 and the number itself.
- Now, such numbers which have only two factors, i.e., 11 and the number itself are called prime numbers.
Prime Factorization
Prime factorization is defined as the product of all the prime factors of a number whose multiplication gives the number itself. Moreover, sometimes to write the prime factors of a number, we may have to repeat the number. So, for example, the factors of 88 are 11 and 22, but to represent 88 we use 8=2×2×28=2×2×2.
How to Calculate Prime Factorization of 8?
Greatest Common Factor
A common factor is a factor that is common to two numbers. So, as the name suggests, a Greatest Common Factor (GCF) is the greatest numbers formed by multiplying the common factors of 2 numbers. A practical use of Greatest Common Factors is for simplifying fractions.
How to Find the Greatest Common Factor (GCF)
To find the Greatest Common Factor, follow these steps:
- First break down both the numbers into their prime factors.
- Now, list out the common factors between those 2 numbers. Then you can multiply the common factors to generate the Greatest Common Factor.
- Also, if you find that there are no common prime factors between these numbers, then the GCF is always 1.
For example, 100=2×2×5×5100=2×2×5×5 and 50=2×5×550=2×5×5. so GCF(100,50)=2×5×5=50GCF(100,50)=2×5×5=50.
Find the Greatest Common Factor Video
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Related Topics
How to Find the Least Common Multiple
How to Factor Numbers
How to Find the Least Common Multiple
Exercises for Greatest Common Factor
1) GCF(33, 45) =GCF(33, 45) =
2) GCF(26, 14) =GCF(26, 14) =
3) GCF(11, 14) =GCF(11, 14) =
4) GCF(12, 42) =GCF(12, 42) =
5) GCF(45, 42) =GCF(45, 42) =
6) GCF(42, 34) =GCF(42, 34) =
7) GCF(26, 52) =GCF(26, 52) =
8) GCF(90, 27) =GCF(90, 27) =
9) GCF(92, 80) =GCF(92, 80) =
10) GCF(27, 18) =GCF(27, 18) =
1) GCF(33, 45) = 3GCF(33, 45) = 3
2) GCF(26, 14) = 2
3) GCF(11, 14) = 1
4) GCF(12, 42) = 6
5) GCF(45, 42) = 3
6) GCF(42, 34) = 2
7) GCF(26, 52) = 26
8) GCF(90, 27) = 9
9) GCF(92, 80) = 4
10) GCF(27, 18) = 9
Greatest Common Factor Quiz