How to Find GCF of 920/224, 6177/416?

GCF of 920/224, 6177/416

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 920/224, 6177/416 i.e 1/2912 easily. The following is the detailed procedure to determine the greatest common factor of fractions 920/224, 6177/416.

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 920/224,6177/416?

Given fractions are 920/224,6177/416

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 920/224,6177/416, numerators are 920,6177

Denominators are 224,416

The GCF of 920,6177 is 1 .

LCM of 224,416 is 2912.

The greatest common factor of 920/224,6177/416 = [GCF of 920,6177]/[LCM of 224,416]= 1/2912

Therefore, the GCF of 920/224,6177/416 is 1/2912.

Greatest Common Factor of 920,6177

To find the highest common factor of 920,6177, 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 6177 are 1, 3, 29, 71, 87, 213, 2059, 6177

The HCF of 920,6177 is 1.

Lets's calculate GCF of 920,6177

Greatest Common Factor (GCF) of 920,6177 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 920,6177 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 6177

1,3,29,71,87,213,2059,6177

Greatest Common Factor

We found the factors 920,6177 . The biggest common factor number is the GCF number.
So the greatest common factor 920,6177 is 1.

Lets's calculate LCM of 224,416

Lowest Common Multiple of 224,416 using Common Division

2	224, 416
2	112, 208
2	56, 104
2	28, 52
2	14, 26
	7, 13

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 7 x 13 = 2912

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2912

Therefore, the GCF of Fractions 920/224,6177/416 is 1/2912

Least Common Multiple of 224,416 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 224,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(224,416) = 32

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

GCF(224,416) x common factors =32 x 1 = 32

LCM(224,416) = ( 224 × 416 ) / 32

LCM(224,416) = 93184 / 32

LCM(224,416) = 2912

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FAQs on GCF of Fractions of 920/224, 6177/416

1. What is the HCF of 920,6177?

The HCF of 920,6177 is 1

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 920/224, 6177/416?

Answer: GCF of Numerators as per given numbers 920/224, 6177/416 is

GCF of Numerators i.e. for 920,6177 is 1

LCM of denominators i.e. for 224,416 is 2912.

Thus, GCF of Fractions is 1/2912.Finally, GCF of Fractions for 920/224, 6177/416 is 1/2912.