GCF of 8412/572, 8475/422
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8412/572, 8475/422 i.e 3/120692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8412/572, 8475/422.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 8412/572,8475/422?
Given fractions are 8412/572,8475/422
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 8412/572,8475/422, numerators are 8412,8475
Denominators are 572,422
The GCF of 8412,8475 is 3 .
LCM of 572,422 is 120692.
The greatest common factor of 8412/572,8475/422 = [GCF of 8412,8475]/[LCM of 572,422]= 3/120692
Therefore, the GCF of 8412/572,8475/422 is 3/120692.
To find the highest common factor of 8412,8475, we have to find the factors of both numbers and list the highest common factor.
The factors of 8412 are 1, 2, 3, 4, 6, 12, 701, 1402, 2103, 2804, 4206, 8412
The factors of 8475 are 1, 3, 5, 15, 25, 75, 113, 339, 565, 1695, 2825, 8475
The HCF of 8412,8475 is 3.
Lets's calculate GCF of 8412,8475
| 3 | 8412, 8475 |
| 2804, 2825 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 8412,8475 By Matching Biggest Common Factor Method
Now, list down the factors of 8412
:1,2,3,4,6,12,701,1402,2103,2804,4206,8412
Now, list down the factors of 8475
:1,3,5,15,25,75,113,339,565,1695,2825,8475
Greatest Common Factor
We found the factors 8412,8475 . The biggest common factor number is the GCF number.
So the greatest common factor 8412,8475 is 3.
Lets's calculate LCM of 572,422
| 2 | 572, 422 |
| 286, 211 |
∴ So the LCM of the given numbers is 2 x 286 x 211 = 120692
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/120692
Therefore, the GCF of Fractions 8412/572,8475/422 is 3/120692
Least Common Multiple of 572,422 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 572,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(572,422) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(572,422) x common factors =2 x 1 = 2
LCM(572,422) = ( 572 × 422 ) / 2
LCM(572,422) = 241384 / 2
LCM(572,422) = 120692
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FAQs on GCF of Fractions of 8412/572, 8475/422
1. What is the HCF of 8412,8475?
The HCF of 8412,8475 is 3
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 8412/572, 8475/422?
Answer: GCF of Numerators as per given numbers 8412/572, 8475/422 is
GCF of Numerators i.e. for 8412,8475 is 3
LCM of denominators i.e. for 572,422 is 120692.
Thus, GCF of Fractions is 3/120692.Finally, GCF of Fractions for 8412/572, 8475/422 is 3/120692.