How to Find GCF of 42/77, 21/72, 274/780?

GCF of 42/77, 21/72, 274/780

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 42/77, 21/72, 274/780 i.e 1/360360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/77, 21/72, 274/780.

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 42/77,21/72,274/780?

Given fractions are 42/77,21/72,274/780

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 42/77,21/72,274/780, numerators are 42,21,274

Denominators are 77,72,780

The GCF of 42,21,274 is 1 .

LCM of 77,72,780 is 360360.

The greatest common factor of 42/77,21/72,274/780 = [GCF of 42,21,274]/[LCM of 77,72,780]= 1/360360

Therefore, the GCF of 42/77,21/72,274/780 is 1/360360.

Greatest Common Factor of 42,21,274

To find the highest common factor of 42,21,274, we have to find the factors of both numbers and list the highest common factor.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

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

The factors of 274 are 1, 2, 137, 274

The HCF of 42,21,274 is 1.

Lets's calculate GCF of 42,21,274

Greatest Common Factor (GCF) of 42,21,274 By Common Division

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

Greatest Common Factor of 42,21,274 By Matching Biggest Common Factor Method

Now, list down the factors of 42

1,2,3,6,7,14,21,42

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 274

1,2,137,274

Greatest Common Factor

We found the factors 42,21,274 . The biggest common factor number is the GCF number.
So the greatest common factor 42,21,274 is 1.

Lets's calculate LCM of 77,72,780

Lowest Common Multiple of 77,72,780 using Common Division

2	77, 72, 780
2	77, 36, 390
3	77, 18, 195
	77, 6, 65

∴ So the LCM of the given numbers is 2 x 2 x 3 x 77 x 6 x 65 = 360360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/360360

Therefore, the GCF of Fractions 42/77,21/72,274/780 is 1/360360

Least Common Multiple of 77,72,780 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 77,72,780 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(77,72,780) = 1

common factors(in case of two or more numbers have common factors) = 12

GCF(77,72,780) x common factors =1 x 12 = 12

LCM(77,72,780) = ( 77 × 72 × 780 ) / 12

LCM(77,72,780) = 4324320 / 12

LCM(77,72,780) = 360360

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 42/77, 21/72, 274/780

1. What is the HCF of 42,21,274?

The HCF of 42,21,274 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 42/77, 21/72, 274/780?

Answer: GCF of Numerators as per given numbers 42/77, 21/72, 274/780 is

GCF of Numerators i.e. for 42,21,274 is 1

LCM of denominators i.e. for 77,72,780 is 360360.

Thus, GCF of Fractions is 1/360360.Finally, GCF of Fractions for 42/77, 21/72, 274/780 is 1/360360.