How to Find GCF of 21/42, 77/29, 874/856?

GCF of 21/42, 77/29, 874/856

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 21/42, 77/29, 874/856 i.e 1/521304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/42, 77/29, 874/856.

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 21/42,77/29,874/856?

Given fractions are 21/42,77/29,874/856

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 21/42,77/29,874/856, numerators are 21,77,874

Denominators are 42,29,856

The GCF of 21,77,874 is 1 .

LCM of 42,29,856 is 521304.

The greatest common factor of 21/42,77/29,874/856 = [GCF of 21,77,874]/[LCM of 42,29,856]= 1/521304

Therefore, the GCF of 21/42,77/29,874/856 is 1/521304.

Greatest Common Factor of 21,77,874

To find the highest common factor of 21,77,874, we have to find the factors of both numbers and list the highest common factor.

The factors of 21 are 1, 3, 7, 21

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

The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874

The HCF of 21,77,874 is 1.

Lets's calculate GCF of 21,77,874

Greatest Common Factor (GCF) of 21,77,874 By Common Division

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

Greatest Common Factor of 21,77,874 By Matching Biggest Common Factor Method

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 874

1,2,19,23,38,46,437,874

Greatest Common Factor

We found the factors 21,77,874 . The biggest common factor number is the GCF number.
So the greatest common factor 21,77,874 is 1.

Lets's calculate LCM of 42,29,856

Lowest Common Multiple of 42,29,856 using Common Division

2	42, 29, 856
	21, 29, 428

∴ So the LCM of the given numbers is 2 x 21 x 29 x 428 = 521304

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/521304

Therefore, the GCF of Fractions 21/42,77/29,874/856 is 1/521304

Least Common Multiple of 42,29,856 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 42,29,856 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,29,856) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(42,29,856) x common factors =1 x 2 = 2

LCM(42,29,856) = ( 42 × 29 × 856 ) / 2

LCM(42,29,856) = 1042608 / 2

LCM(42,29,856) = 521304

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FAQs on GCF of Fractions of 21/42, 77/29, 874/856

1. What is the HCF of 21,77,874?

The HCF of 21,77,874 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 21/42, 77/29, 874/856?

Answer: GCF of Numerators as per given numbers 21/42, 77/29, 874/856 is

GCF of Numerators i.e. for 21,77,874 is 1

LCM of denominators i.e. for 42,29,856 is 521304.

Thus, GCF of Fractions is 1/521304.Finally, GCF of Fractions for 21/42, 77/29, 874/856 is 1/521304.