GCF of 506/828, 874/130
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 506/828, 874/130 i.e 46/53820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 506/828, 874/130.
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 506/828,874/130?
Given fractions are 506/828,874/130
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 506/828,874/130, numerators are 506,874
Denominators are 828,130
The GCF of 506,874 is 46 .
LCM of 828,130 is 53820.
The greatest common factor of 506/828,874/130 = [GCF of 506,874]/[LCM of 828,130]= 46/53820
Therefore, the GCF of 506/828,874/130 is 46/53820.
To find the highest common factor of 506,874, we have to find the factors of both numbers and list the highest common factor.
The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506
The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874
The HCF of 506,874 is 46.
Lets's calculate GCF of 506,874
| 2 | 506, 874 |
| 23 | 253, 437 |
| 11, 19 |
∴ So the GCF of the given numbers is 2 x 23 = 46
Greatest Common Factor of 506,874 By Matching Biggest Common Factor Method
Now, list down the factors of 506
:1,2,11,22,23,46,253,506
Now, list down the factors of 874
:1,2,19,23,38,46,437,874
Greatest Common Factor
We found the factors 506,874 . The biggest common factor number is the GCF number.
So the greatest common factor 506,874 is 46.
Lets's calculate LCM of 828,130
| 2 | 828, 130 |
| 414, 65 |
∴ So the LCM of the given numbers is 2 x 414 x 65 = 53820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/53820
Therefore, the GCF of Fractions 506/828,874/130 is 46/53820
Least Common Multiple of 828,130 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 828,130 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(828,130) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(828,130) x common factors =2 x 1 = 2
LCM(828,130) = ( 828 × 130 ) / 2
LCM(828,130) = 107640 / 2
LCM(828,130) = 53820
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FAQs on GCF of Fractions of 506/828, 874/130
1. What is the HCF of 506,874?
The HCF of 506,874 is 46
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 506/828, 874/130?
Answer: GCF of Numerators as per given numbers 506/828, 874/130 is
GCF of Numerators i.e. for 506,874 is 46
LCM of denominators i.e. for 828,130 is 53820.
Thus, GCF of Fractions is 46/53820.Finally, GCF of Fractions for 506/828, 874/130 is 46/53820.