This is the greatest Common Factor between 2 or more numbers.
To find the GCF of numbers (let’s say 8 & 10):
We will find the prime factors of each number.So that,
35 = 5×7
15 = 5×3
There is only one factor in common. That is 5. Therefore, GCF = 5
We will find the prime factors of each number.So that,
35 = 5×7
10 = 5×2
There is only one factor in common. That is 5. Therefore, GCF = 5
We will find the prime factors of each number.So that,
25 = 5 × 5
125 = 5 × 5 x 5
There are two common factor 5 and 5 and their multiplication is 25. Therefore, GCF = 25
We will find the prime factors of each number.So that,
15 = 5 × 3
30 = 5 × 3 x 2
There are two common factor 5 and 3 and their multiplication is 15. Therefore, GCF = 15
We will find the prime factors of each number.
So that,
240 = 24 × 10
= 3 × 8 × 10
= 3 × 2 × 2 × 2 × 2 × 5
150 = 15 × 10
= 5 × 3 × 2 × 5
Identify the common factors in both numbers. They are 3, 2 and 5. To find GCF of
the numbers multiply the common factors between two numbers. GCF=3×2×5= 30
If you have given three numbers 125, 450 and 525.
To find GCF of the numbers we will find the prime factors of each number.
So that,
125 = 25 × 5
= 5 × 5 × 5
450 = 45 × 10
= 5 × 9 × 2 × 5
= 5 × 3 × 3 × 2 × 5
525 = 5 × 5 × 21
5 × 5 × 7 × 3
I can see that the all numbers have a factor of 5, 5 in common. Multiply these numbers
5 × 5 = 25.
So that, GCF = 25
Polynomials are Terms containing multiples of various variable( x, y, z etc.)
To find the GCF of all the terms in the polynomial
GCF of x2 and x3 is x2.
GCF of 2y2& 4y is 2y.
In the polynomial 6x^{3}y^{2, }8x^{2}y and 4xyz for
example, x and y appear in all three terms, so they are both part of the GCF. Z
appears in only one term, so do not include it in the GCF.
Use each variable with the lowest exponent it has in the polynomial for the GCF.
In 6x^{3}y^{2, }8x^{2}y and 4xyz. 1 is the lowest
exponent with x, The lowest exponent of y is 1. This means xy is part of the GCF
for this polynomial.
The coefficients of 6x^{3}y^{2, }8x^{2}y and 4xyz are
6, 8, and 4. The prime factorizations are 2×3, 2× 2 × 2 and 2× 2,
respectively. Since only 2 is common factor in all, it is the GCF.
Write the GCF of the coefficients before the GCF of the variables to get the complete
GCF for the polynomial.
Therefore, GCF of 6x^{3}y^{2, }8x^{2}y and 4xyz is 2xy.
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