GCF of 564/70, 252/5102
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 564/70, 252/5102 i.e 12/178570 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/70, 252/5102.
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 564/70,252/5102?
Given fractions are 564/70,252/5102
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 564/70,252/5102, numerators are 564,252
Denominators are 70,5102
The GCF of 564,252 is 12 .
LCM of 70,5102 is 178570.
The greatest common factor of 564/70,252/5102 = [GCF of 564,252]/[LCM of 70,5102]= 12/178570
Therefore, the GCF of 564/70,252/5102 is 12/178570.
To find the highest common factor of 564,252, we have to find the factors of both numbers and list the highest common factor.
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
The HCF of 564,252 is 12.
Lets's calculate GCF of 564,252
| 2 | 564, 252 |
| 2 | 282, 126 |
| 3 | 141, 63 |
| 47, 21 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 564,252 By Matching Biggest Common Factor Method
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Now, list down the factors of 252
:1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252
Greatest Common Factor
We found the factors 564,252 . The biggest common factor number is the GCF number.
So the greatest common factor 564,252 is 12.
Lets's calculate LCM of 70,5102
| 2 | 70, 5102 |
| 35, 2551 |
∴ So the LCM of the given numbers is 2 x 35 x 2551 = 178570
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/178570
Therefore, the GCF of Fractions 564/70,252/5102 is 12/178570
Least Common Multiple of 70,5102 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 70,5102 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,5102) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(70,5102) x common factors =2 x 1 = 2
LCM(70,5102) = ( 70 × 5102 ) / 2
LCM(70,5102) = 357140 / 2
LCM(70,5102) = 178570
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 564/70, 252/5102
1. What is the HCF of 564,252?
The HCF of 564,252 is 12
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 564/70, 252/5102?
Answer: GCF of Numerators as per given numbers 564/70, 252/5102 is
GCF of Numerators i.e. for 564,252 is 12
LCM of denominators i.e. for 70,5102 is 178570.
Thus, GCF of Fractions is 12/178570.Finally, GCF of Fractions for 564/70, 252/5102 is 12/178570.