How to Find GCF of 124/960, 8414/7680?

GCF of 124/960, 8414/7680

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 124/960, 8414/7680 i.e 2/7680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 124/960, 8414/7680.

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 124/960,8414/7680?

Given fractions are 124/960,8414/7680

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 124/960,8414/7680, numerators are 124,8414

Denominators are 960,7680

The GCF of 124,8414 is 2 .

LCM of 960,7680 is 7680.

The greatest common factor of 124/960,8414/7680 = [GCF of 124,8414]/[LCM of 960,7680]= 2/7680

Therefore, the GCF of 124/960,8414/7680 is 2/7680.

Greatest Common Factor of 124,8414

To find the highest common factor of 124,8414, we have to find the factors of both numbers and list the highest common factor.

The factors of 124 are 1, 2, 4, 31, 62, 124

The factors of 8414 are 1, 2, 7, 14, 601, 1202, 4207, 8414

The HCF of 124,8414 is 2.

Lets's calculate GCF of 124,8414

Greatest Common Factor (GCF) of 124,8414 By Common Division

2	124, 8414
	62, 4207

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

Greatest Common Factor of 124,8414 By Matching Biggest Common Factor Method

Now, list down the factors of 124

1,2,4,31,62,124

Now, list down the factors of 8414

1,2,7,14,601,1202,4207,8414

Greatest Common Factor

We found the factors 124,8414 . The biggest common factor number is the GCF number.
So the greatest common factor 124,8414 is 2.

Lets's calculate LCM of 960,7680

Lowest Common Multiple of 960,7680 using Common Division

2	960, 7680
2	480, 3840
2	240, 1920
2	120, 960
2	60, 480
2	30, 240
3	15, 120
5	5, 40
	1, 8

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 1 x 8 = 7680

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7680

Therefore, the GCF of Fractions 124/960,8414/7680 is 2/7680

Least Common Multiple of 960,7680 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 960,7680 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(960,7680) = 960

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

GCF(960,7680) x common factors =960 x 1 = 960

LCM(960,7680) = ( 960 × 7680 ) / 960

LCM(960,7680) = 7372800 / 960

LCM(960,7680) = 7680

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FAQs on GCF of Fractions of 124/960, 8414/7680

1. What is the HCF of 124,8414?

The HCF of 124,8414 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 124/960, 8414/7680?

Answer: GCF of Numerators as per given numbers 124/960, 8414/7680 is

GCF of Numerators i.e. for 124,8414 is 2

LCM of denominators i.e. for 960,7680 is 7680.

Thus, GCF of Fractions is 2/7680.Finally, GCF of Fractions for 124/960, 8414/7680 is 2/7680.