GCF of 527/420, 496/334
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 527/420, 496/334 i.e 31/70140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 527/420, 496/334.
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 527/420,496/334?
Given fractions are 527/420,496/334
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 527/420,496/334, numerators are 527,496
Denominators are 420,334
The GCF of 527,496 is 31 .
LCM of 420,334 is 70140.
The greatest common factor of 527/420,496/334 = [GCF of 527,496]/[LCM of 420,334]= 31/70140
Therefore, the GCF of 527/420,496/334 is 31/70140.
To find the highest common factor of 527,496, we have to find the factors of both numbers and list the highest common factor.
The factors of 527 are 1, 17, 31, 527
The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496
The HCF of 527,496 is 31.
Lets's calculate GCF of 527,496
| 31 | 527, 496 |
| 17, 16 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 527,496 By Matching Biggest Common Factor Method
Now, list down the factors of 527
:1,17,31,527
Now, list down the factors of 496
:1,2,4,8,16,31,62,124,248,496
Greatest Common Factor
We found the factors 527,496 . The biggest common factor number is the GCF number.
So the greatest common factor 527,496 is 31.
Lets's calculate LCM of 420,334
| 2 | 420, 334 |
| 210, 167 |
∴ So the LCM of the given numbers is 2 x 210 x 167 = 70140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/70140
Therefore, the GCF of Fractions 527/420,496/334 is 31/70140
Least Common Multiple of 420,334 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 420,334 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,334) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(420,334) x common factors =2 x 1 = 2
LCM(420,334) = ( 420 × 334 ) / 2
LCM(420,334) = 140280 / 2
LCM(420,334) = 70140
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FAQs on GCF of Fractions of 527/420, 496/334
1. What is the HCF of 527,496?
The HCF of 527,496 is 31
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 527/420, 496/334?
Answer: GCF of Numerators as per given numbers 527/420, 496/334 is
GCF of Numerators i.e. for 527,496 is 31
LCM of denominators i.e. for 420,334 is 70140.
Thus, GCF of Fractions is 31/70140.Finally, GCF of Fractions for 527/420, 496/334 is 31/70140.