How to Find GCF of 920/124, 8078/164?

GCF of 920/124, 8078/164

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 920/124, 8078/164 i.e 2/5084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 920/124, 8078/164.

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 920/124,8078/164?

Given fractions are 920/124,8078/164

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 920/124,8078/164, numerators are 920,8078

Denominators are 124,164

The GCF of 920,8078 is 2 .

LCM of 124,164 is 5084.

The greatest common factor of 920/124,8078/164 = [GCF of 920,8078]/[LCM of 124,164]= 2/5084

Therefore, the GCF of 920/124,8078/164 is 2/5084.

Greatest Common Factor of 920,8078

To find the highest common factor of 920,8078, we have to find the factors of both numbers and list the highest common factor.

The factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920

The factors of 8078 are 1, 2, 7, 14, 577, 1154, 4039, 8078

The HCF of 920,8078 is 2.

Lets's calculate GCF of 920,8078

Greatest Common Factor (GCF) of 920,8078 By Common Division

2	920, 8078
	460, 4039

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 920,8078 By Matching Biggest Common Factor Method

Now, list down the factors of 920

1,2,4,5,8,10,20,23,40,46,92,115,184,230,460,920

Now, list down the factors of 8078

1,2,7,14,577,1154,4039,8078

Greatest Common Factor

We found the factors 920,8078 . The biggest common factor number is the GCF number.
So the greatest common factor 920,8078 is 2.

Lets's calculate LCM of 124,164

Lowest Common Multiple of 124,164 using Common Division

2	124, 164
2	62, 82
	31, 41

∴ So the LCM of the given numbers is 2 x 2 x 31 x 41 = 5084

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5084

Therefore, the GCF of Fractions 920/124,8078/164 is 2/5084

Least Common Multiple of 124,164 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 124,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(124,164) = 4

common factors(in case of two or more numbers have common factors) = 1

GCF(124,164) x common factors =4 x 1 = 4

LCM(124,164) = ( 124 × 164 ) / 4

LCM(124,164) = 20336 / 4

LCM(124,164) = 5084

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FAQs on GCF of Fractions of 920/124, 8078/164

1. What is the HCF of 920,8078?

The HCF of 920,8078 is 2

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 920/124, 8078/164?

Answer: GCF of Numerators as per given numbers 920/124, 8078/164 is

GCF of Numerators i.e. for 920,8078 is 2

LCM of denominators i.e. for 124,164 is 5084.

Thus, GCF of Fractions is 2/5084.Finally, GCF of Fractions for 920/124, 8078/164 is 2/5084.