How to Find GCF of 31/65, 22/312, 221/870?

GCF of 31/65, 22/312, 221/870

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 31/65, 22/312, 221/870 i.e 1/45240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/65, 22/312, 221/870.

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 31/65,22/312,221/870?

Given fractions are 31/65,22/312,221/870

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 31/65,22/312,221/870, numerators are 31,22,221

Denominators are 65,312,870

The GCF of 31,22,221 is 1 .

LCM of 65,312,870 is 45240.

The greatest common factor of 31/65,22/312,221/870 = [GCF of 31,22,221]/[LCM of 65,312,870]= 1/45240

Therefore, the GCF of 31/65,22/312,221/870 is 1/45240.

Greatest Common Factor of 31,22,221

To find the highest common factor of 31,22,221, we have to find the factors of both numbers and list the highest common factor.

The factors of 31 are 1, 31

The factors of 22 are 1, 2, 11, 22

The factors of 221 are 1, 13, 17, 221

The HCF of 31,22,221 is 1.

Lets's calculate GCF of 31,22,221

Greatest Common Factor (GCF) of 31,22,221 By Common Division

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

Greatest Common Factor of 31,22,221 By Matching Biggest Common Factor Method

Now, list down the factors of 31

1,31

Now, list down the factors of 22

1,2,11,22

Now, list down the factors of 221

1,13,17,221

Greatest Common Factor

We found the factors 31,22,221 . The biggest common factor number is the GCF number.
So the greatest common factor 31,22,221 is 1.

Lets's calculate LCM of 65,312,870

Lowest Common Multiple of 65,312,870 using Common Division

2	65, 312, 870
3	65, 156, 435
5	65, 52, 145
13	13, 52, 29
	1, 4, 29

∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 1 x 4 x 29 = 45240

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/45240

Therefore, the GCF of Fractions 31/65,22/312,221/870 is 1/45240

Least Common Multiple of 65,312,870 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 65,312,870 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,312,870) = 1

common factors(in case of two or more numbers have common factors) = 390

GCF(65,312,870) x common factors =1 x 390 = 390

LCM(65,312,870) = ( 65 × 312 × 870 ) / 390

LCM(65,312,870) = 17643600 / 390

LCM(65,312,870) = 45240

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FAQs on GCF of Fractions of 31/65, 22/312, 221/870

1. What is the HCF of 31,22,221?

The HCF of 31,22,221 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 31/65, 22/312, 221/870?

Answer: GCF of Numerators as per given numbers 31/65, 22/312, 221/870 is

GCF of Numerators i.e. for 31,22,221 is 1

LCM of denominators i.e. for 65,312,870 is 45240.

Thus, GCF of Fractions is 1/45240.Finally, GCF of Fractions for 31/65, 22/312, 221/870 is 1/45240.