How to Find GCF of 49/77, 39/78, 676/72?

GCF of 49/77, 39/78, 676/72

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 49/77, 39/78, 676/72 i.e 1/72072 easily. The following is the detailed procedure to determine the greatest common factor of fractions 49/77, 39/78, 676/72.

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 49/77,39/78,676/72?

Given fractions are 49/77,39/78,676/72

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 49/77,39/78,676/72, numerators are 49,39,676

Denominators are 77,78,72

The GCF of 49,39,676 is 1 .

LCM of 77,78,72 is 72072.

The greatest common factor of 49/77,39/78,676/72 = [GCF of 49,39,676]/[LCM of 77,78,72]= 1/72072

Therefore, the GCF of 49/77,39/78,676/72 is 1/72072.

Greatest Common Factor of 49,39,676

To find the highest common factor of 49,39,676, we have to find the factors of both numbers and list the highest common factor.

The factors of 49 are 1, 7, 49

The factors of 39 are 1, 3, 13, 39

The factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676

The HCF of 49,39,676 is 1.

Lets's calculate GCF of 49,39,676

Greatest Common Factor (GCF) of 49,39,676 By Common Division

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

Greatest Common Factor of 49,39,676 By Matching Biggest Common Factor Method

Now, list down the factors of 49

1,7,49

Now, list down the factors of 39

1,3,13,39

Now, list down the factors of 676

1,2,4,13,26,52,169,338,676

Greatest Common Factor

We found the factors 49,39,676 . The biggest common factor number is the GCF number.
So the greatest common factor 49,39,676 is 1.

Lets's calculate LCM of 77,78,72

Lowest Common Multiple of 77,78,72 using Common Division

2	77, 78, 72
3	77, 39, 36
	77, 13, 12

∴ So the LCM of the given numbers is 2 x 3 x 77 x 13 x 12 = 72072

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/72072

Therefore, the GCF of Fractions 49/77,39/78,676/72 is 1/72072

Least Common Multiple of 77,78,72 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 77,78,72 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(77,78,72) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(77,78,72) x common factors =1 x 6 = 6

LCM(77,78,72) = ( 77 × 78 × 72 ) / 6

LCM(77,78,72) = 432432 / 6

LCM(77,78,72) = 72072

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FAQs on GCF of Fractions of 49/77, 39/78, 676/72

1. What is the HCF of 49,39,676?

The HCF of 49,39,676 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 49/77, 39/78, 676/72?

Answer: GCF of Numerators as per given numbers 49/77, 39/78, 676/72 is

GCF of Numerators i.e. for 49,39,676 is 1

LCM of denominators i.e. for 77,78,72 is 72072.

Thus, GCF of Fractions is 1/72072.Finally, GCF of Fractions for 49/77, 39/78, 676/72 is 1/72072.