How to Find GCF of 77/68, 37/78, 51/21?

GCF of 77/68, 37/78, 51/21

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 77/68, 37/78, 51/21 i.e 1/18564 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/68, 37/78, 51/21.

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 77/68,37/78,51/21?

Given fractions are 77/68,37/78,51/21

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 77/68,37/78,51/21, numerators are 77,37,51

Denominators are 68,78,21

The GCF of 77,37,51 is 1 .

LCM of 68,78,21 is 18564.

The greatest common factor of 77/68,37/78,51/21 = [GCF of 77,37,51]/[LCM of 68,78,21]= 1/18564

Therefore, the GCF of 77/68,37/78,51/21 is 1/18564.

Greatest Common Factor of 77,37,51

To find the highest common factor of 77,37,51, we have to find the factors of both numbers and list the highest common factor.

The factors of 77 are 1, 7, 11, 77

The factors of 37 are 1, 37

The factors of 51 are 1, 3, 17, 51

The HCF of 77,37,51 is 1.

Lets's calculate GCF of 77,37,51

Greatest Common Factor (GCF) of 77,37,51 By Common Division

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

Greatest Common Factor of 77,37,51 By Matching Biggest Common Factor Method

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 37

1,37

Now, list down the factors of 51

1,3,17,51

Greatest Common Factor

We found the factors 77,37,51 . The biggest common factor number is the GCF number.
So the greatest common factor 77,37,51 is 1.

Lets's calculate LCM of 68,78,21

Lowest Common Multiple of 68,78,21 using Common Division

2	68, 78, 21
3	34, 39, 21
	34, 13, 7

∴ So the LCM of the given numbers is 2 x 3 x 34 x 13 x 7 = 18564

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18564

Therefore, the GCF of Fractions 77/68,37/78,51/21 is 1/18564

Least Common Multiple of 68,78,21 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 68,78,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,78,21) = 1

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

GCF(68,78,21) x common factors =1 x 6 = 6

LCM(68,78,21) = ( 68 × 78 × 21 ) / 6

LCM(68,78,21) = 111384 / 6

LCM(68,78,21) = 18564

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FAQs on GCF of Fractions of 77/68, 37/78, 51/21

1. What is the HCF of 77,37,51?

The HCF of 77,37,51 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 77/68, 37/78, 51/21?

Answer: GCF of Numerators as per given numbers 77/68, 37/78, 51/21 is

GCF of Numerators i.e. for 77,37,51 is 1

LCM of denominators i.e. for 68,78,21 is 18564.

Thus, GCF of Fractions is 1/18564.Finally, GCF of Fractions for 77/68, 37/78, 51/21 is 1/18564.