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GCF of 231/32, 262/178

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 231/32, 262/178 i.e 1/2848 easily. The following is the detailed procedure to determine the greatest common factor of fractions 231/32, 262/178.

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 231/32,262/178?

Given fractions are 231/32,262/178

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 231/32,262/178, numerators are 231,262

Denominators are 32,178

The GCF of 231,262 is 1 .

LCM of 32,178 is 2848.

The greatest common factor of 231/32,262/178 = [GCF of 231,262]/[LCM of 32,178]= 1/2848

Therefore, the GCF of 231/32,262/178 is 1/2848.

Greatest Common Factor of 231,262

To find the highest common factor of 231,262, we have to find the factors of both numbers and list the highest common factor.

The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231

The factors of 262 are 1, 2, 131, 262

The HCF of 231,262 is 1.

Lets's calculate GCF of 231,262

Greatest Common Factor (GCF) of 231,262 By Common Division

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

Greatest Common Factor of 231,262 By Matching Biggest Common Factor Method

Greatest Common Factor of 231,262 By Matching Biggest Common Factor Method

Now, list down the factors of 231

:

1,3,7,11,21,33,77,231

Now, list down the factors of 262

:

1,2,131,262

Greatest Common Factor

We found the factors 231,262 . The biggest common factor number is the GCF number.
So the greatest common factor 231,262 is 1.

Lets's calculate LCM of 32,178

Lowest Common Multiple of 32,178 using Common Division

2 32, 178
16, 89

∴ So the LCM of the given numbers is 2 x 16 x 89 = 2848

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2848

Therefore, the GCF of Fractions 231/32,262/178 is 1/2848

Least Common Multiple of 32,178 with GCF Formula

Least Common Multiple of 32,178 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 32,178 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(32,178) = 2

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

GCF(32,178) x common factors =2 x 1 = 2

LCM(32,178) = ( 32 × 178 ) / 2

LCM(32,178) = 5696 / 2

LCM(32,178) = 2848


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FAQs on GCF of Fractions of 231/32, 262/178

1. What is the HCF of 231,262?

The HCF of 231,262 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 231/32, 262/178?

Answer: GCF of Numerators as per given numbers 231/32, 262/178 is

GCF of Numerators i.e. for 231,262 is 1

LCM of denominators i.e. for 32,178 is 2848.

Thus, GCF of Fractions is 1/2848.Finally, GCF of Fractions for 231/32, 262/178 is 1/2848.