How to Find GCF of 72/676, 31/245, 208/284?

GCF of 72/676, 31/245, 208/284

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 72/676, 31/245, 208/284 i.e 1/11759020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/676, 31/245, 208/284.

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 72/676,31/245,208/284?

Given fractions are 72/676,31/245,208/284

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 72/676,31/245,208/284, numerators are 72,31,208

Denominators are 676,245,284

The GCF of 72,31,208 is 1 .

LCM of 676,245,284 is 11759020.

The greatest common factor of 72/676,31/245,208/284 = [GCF of 72,31,208]/[LCM of 676,245,284]= 1/11759020

Therefore, the GCF of 72/676,31/245,208/284 is 1/11759020.

Greatest Common Factor of 72,31,208

To find the highest common factor of 72,31,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The factors of 31 are 1, 31

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 72,31,208 is 1.

Lets's calculate GCF of 72,31,208

Greatest Common Factor (GCF) of 72,31,208 By Common Division

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

Greatest Common Factor of 72,31,208 By Matching Biggest Common Factor Method

Now, list down the factors of 72

1,2,3,4,6,8,9,12,18,24,36,72

Now, list down the factors of 31

1,31

Now, list down the factors of 208

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 72,31,208 . The biggest common factor number is the GCF number.
So the greatest common factor 72,31,208 is 1.

Lets's calculate LCM of 676,245,284

Lowest Common Multiple of 676,245,284 using Common Division

2	676, 245, 284
2	338, 245, 142
	169, 245, 71

∴ So the LCM of the given numbers is 2 x 2 x 169 x 245 x 71 = 11759020

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11759020

Therefore, the GCF of Fractions 72/676,31/245,208/284 is 1/11759020

Least Common Multiple of 676,245,284 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 676,245,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(676,245,284) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(676,245,284) x common factors =1 x 4 = 4

LCM(676,245,284) = ( 676 × 245 × 284 ) / 4

LCM(676,245,284) = 47036080 / 4

LCM(676,245,284) = 11759020

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FAQs on GCF of Fractions of 72/676, 31/245, 208/284

1. What is the HCF of 72,31,208?

The HCF of 72,31,208 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 72/676, 31/245, 208/284?

Answer: GCF of Numerators as per given numbers 72/676, 31/245, 208/284 is

GCF of Numerators i.e. for 72,31,208 is 1

LCM of denominators i.e. for 676,245,284 is 11759020.

Thus, GCF of Fractions is 1/11759020.Finally, GCF of Fractions for 72/676, 31/245, 208/284 is 1/11759020.