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GCF of 317/72, 208/420

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 317/72, 208/420 i.e 1/2520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 317/72, 208/420.

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 317/72,208/420?

Given fractions are 317/72,208/420

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 317/72,208/420, numerators are 317,208

Denominators are 72,420

The GCF of 317,208 is 1 .

LCM of 72,420 is 2520.

The greatest common factor of 317/72,208/420 = [GCF of 317,208]/[LCM of 72,420]= 1/2520

Therefore, the GCF of 317/72,208/420 is 1/2520.

Greatest Common Factor of 317,208

To find the highest common factor of 317,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 317 are 1, 317

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 317,208 is 1.

Lets's calculate GCF of 317,208

Greatest Common Factor (GCF) of 317,208 By Common Division

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

Greatest Common Factor of 317,208 By Matching Biggest Common Factor Method

Greatest Common Factor of 317,208 By Matching Biggest Common Factor Method

Now, list down the factors of 317

:

1,317

Now, list down the factors of 208

:

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 317,208 . The biggest common factor number is the GCF number.
So the greatest common factor 317,208 is 1.

Lets's calculate LCM of 72,420

Lowest Common Multiple of 72,420 using Common Division

2 72, 420
2 36, 210
3 18, 105
6, 35

∴ So the LCM of the given numbers is 2 x 2 x 3 x 6 x 35 = 2520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2520

Therefore, the GCF of Fractions 317/72,208/420 is 1/2520

Least Common Multiple of 72,420 with GCF Formula

Least Common Multiple of 72,420 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 72,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(72,420) = 12

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

GCF(72,420) x common factors =12 x 1 = 12

LCM(72,420) = ( 72 × 420 ) / 12

LCM(72,420) = 30240 / 12

LCM(72,420) = 2520


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FAQs on GCF of Fractions of 317/72, 208/420

1. What is the HCF of 317,208?

The HCF of 317,208 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 317/72, 208/420?

Answer: GCF of Numerators as per given numbers 317/72, 208/420 is

GCF of Numerators i.e. for 317,208 is 1

LCM of denominators i.e. for 72,420 is 2520.

Thus, GCF of Fractions is 1/2520.Finally, GCF of Fractions for 317/72, 208/420 is 1/2520.