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GCF of 532/47, 308/217

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 532/47, 308/217 i.e 28/10199 easily. The following is the detailed procedure to determine the greatest common factor of fractions 532/47, 308/217.

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 532/47,308/217?

Given fractions are 532/47,308/217

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 532/47,308/217, numerators are 532,308

Denominators are 47,217

The GCF of 532,308 is 28 .

LCM of 47,217 is 10199.

The greatest common factor of 532/47,308/217 = [GCF of 532,308]/[LCM of 47,217]= 28/10199

Therefore, the GCF of 532/47,308/217 is 28/10199.

Greatest Common Factor of 532,308

To find the highest common factor of 532,308, we have to find the factors of both numbers and list the highest common factor.

The factors of 532 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 532

The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

The HCF of 532,308 is 28.

Lets's calculate GCF of 532,308

Greatest Common Factor (GCF) of 532,308 By Common Division

2 532, 308
2 266, 154
7 133, 77
19, 11

∴ So the GCF of the given numbers is 2 x 2 x 7 = 28

Greatest Common Factor of 532,308 By Matching Biggest Common Factor Method

Greatest Common Factor of 532,308 By Matching Biggest Common Factor Method

Now, list down the factors of 532

:

1,2,4,7,14,19,28,38,76,133,266,532

Now, list down the factors of 308

:

1,2,4,7,11,14,22,28,44,77,154,308

Greatest Common Factor

We found the factors 532,308 . The biggest common factor number is the GCF number.
So the greatest common factor 532,308 is 28.

Lets's calculate LCM of 47,217

Lowest Common Multiple of 47,217 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 10199

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/10199

Therefore, the GCF of Fractions 532/47,308/217 is 28/10199

Least Common Multiple of 47,217 with GCF Formula

Least Common Multiple of 47,217 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 47,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(47,217) = 1

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

GCF(47,217) x common factors =1 x 1 = 1

LCM(47,217) = ( 47 × 217 ) / 1

LCM(47,217) = 10199 / 1

LCM(47,217) = 10199


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FAQs on GCF of Fractions of 532/47, 308/217

1. What is the HCF of 532,308?

The HCF of 532,308 is 28

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 532/47, 308/217?

Answer: GCF of Numerators as per given numbers 532/47, 308/217 is

GCF of Numerators i.e. for 532,308 is 28

LCM of denominators i.e. for 47,217 is 10199.

Thus, GCF of Fractions is 28/10199.Finally, GCF of Fractions for 532/47, 308/217 is 28/10199.