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GCF of 420/77, 281/406

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 420/77, 281/406 i.e 1/4466 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/77, 281/406.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 420/77,281/406?

Given fractions are 420/77,281/406

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 420/77,281/406, numerators are 420,281

Denominators are 77,406

The GCF of 420,281 is 1 .

LCM of 77,406 is 4466.

The greatest common factor of 420/77,281/406 = [GCF of 420,281]/[LCM of 77,406]= 1/4466

Therefore, the GCF of 420/77,281/406 is 1/4466.

Greatest Common Factor of 420,281

To find the highest common factor of 420,281, we have to find the factors of both numbers and list the highest common factor.

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

The factors of 281 are 1, 281

The HCF of 420,281 is 1.

Lets's calculate GCF of 420,281

Greatest Common Factor (GCF) of 420,281 By Common Division

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

Greatest Common Factor of 420,281 By Matching Biggest Common Factor Method

Greatest Common Factor of 420,281 By Matching Biggest Common Factor Method

Now, list down the factors of 420

:

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Now, list down the factors of 281

:

1,281

Greatest Common Factor

We found the factors 420,281 . The biggest common factor number is the GCF number.
So the greatest common factor 420,281 is 1.

Lets's calculate LCM of 77,406

Lowest Common Multiple of 77,406 using Common Division

7 77, 406
11, 58

∴ So the LCM of the given numbers is 7 x 11 x 58 = 4466

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4466

Therefore, the GCF of Fractions 420/77,281/406 is 1/4466

Least Common Multiple of 77,406 with GCF Formula

Least Common Multiple of 77,406 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 77,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(77,406) = 7

common factors(in case of two or more numbers have common factors) = 1

GCF(77,406) x common factors =7 x 1 = 7

LCM(77,406) = ( 77 × 406 ) / 7

LCM(77,406) = 31262 / 7

LCM(77,406) = 4466


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FAQs on GCF of Fractions of 420/77, 281/406

1. What is the HCF of 420,281?

The HCF of 420,281 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 420/77, 281/406?

Answer: GCF of Numerators as per given numbers 420/77, 281/406 is

GCF of Numerators i.e. for 420,281 is 1

LCM of denominators i.e. for 77,406 is 4466.

Thus, GCF of Fractions is 1/4466.Finally, GCF of Fractions for 420/77, 281/406 is 1/4466.