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GCF of 421/40, 870/144

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 421/40, 870/144 i.e 1/720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 421/40, 870/144.

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 421/40,870/144?

Given fractions are 421/40,870/144

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 421/40,870/144, numerators are 421,870

Denominators are 40,144

The GCF of 421,870 is 1 .

LCM of 40,144 is 720.

The greatest common factor of 421/40,870/144 = [GCF of 421,870]/[LCM of 40,144]= 1/720

Therefore, the GCF of 421/40,870/144 is 1/720.

Greatest Common Factor of 421,870

To find the highest common factor of 421,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 421 are 1, 421

The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

The HCF of 421,870 is 1.

Lets's calculate GCF of 421,870

Greatest Common Factor (GCF) of 421,870 By Common Division

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

Greatest Common Factor of 421,870 By Matching Biggest Common Factor Method

Greatest Common Factor of 421,870 By Matching Biggest Common Factor Method

Now, list down the factors of 421

:

1,421

Now, list down the factors of 870

:

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Greatest Common Factor

We found the factors 421,870 . The biggest common factor number is the GCF number.
So the greatest common factor 421,870 is 1.

Lets's calculate LCM of 40,144

Lowest Common Multiple of 40,144 using Common Division

2 40, 144
2 20, 72
2 10, 36
5, 18

∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 18 = 720

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/720

Therefore, the GCF of Fractions 421/40,870/144 is 1/720

Least Common Multiple of 40,144 with GCF Formula

Least Common Multiple of 40,144 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 40,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,144) = 8

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

GCF(40,144) x common factors =8 x 1 = 8

LCM(40,144) = ( 40 × 144 ) / 8

LCM(40,144) = 5760 / 8

LCM(40,144) = 720


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FAQs on GCF of Fractions of 421/40, 870/144

1. What is the HCF of 421,870?

The HCF of 421,870 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 421/40, 870/144?

Answer: GCF of Numerators as per given numbers 421/40, 870/144 is

GCF of Numerators i.e. for 421,870 is 1

LCM of denominators i.e. for 40,144 is 720.

Thus, GCF of Fractions is 1/720.Finally, GCF of Fractions for 421/40, 870/144 is 1/720.