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GCF of 178/78, 216/253

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 178/78, 216/253 i.e 2/19734 easily. The following is the detailed procedure to determine the greatest common factor of fractions 178/78, 216/253.

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 178/78,216/253?

Given fractions are 178/78,216/253

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 178/78,216/253, numerators are 178,216

Denominators are 78,253

The GCF of 178,216 is 2 .

LCM of 78,253 is 19734.

The greatest common factor of 178/78,216/253 = [GCF of 178,216]/[LCM of 78,253]= 2/19734

Therefore, the GCF of 178/78,216/253 is 2/19734.

Greatest Common Factor of 178,216

To find the highest common factor of 178,216, we have to find the factors of both numbers and list the highest common factor.

The factors of 178 are 1, 2, 89, 178

The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

The HCF of 178,216 is 2.

Lets's calculate GCF of 178,216

Greatest Common Factor (GCF) of 178,216 By Common Division

2 178, 216
89, 108

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 178,216 By Matching Biggest Common Factor Method

Greatest Common Factor of 178,216 By Matching Biggest Common Factor Method

Now, list down the factors of 178

:

1,2,89,178

Now, list down the factors of 216

:

1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216

Greatest Common Factor

We found the factors 178,216 . The biggest common factor number is the GCF number.
So the greatest common factor 178,216 is 2.

Lets's calculate LCM of 78,253

Lowest Common Multiple of 78,253 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 19734

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/19734

Therefore, the GCF of Fractions 178/78,216/253 is 2/19734

Least Common Multiple of 78,253 with GCF Formula

Least Common Multiple of 78,253 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 78,253 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,253) = 1

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

GCF(78,253) x common factors =1 x 1 = 1

LCM(78,253) = ( 78 × 253 ) / 1

LCM(78,253) = 19734 / 1

LCM(78,253) = 19734


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FAQs on GCF of Fractions of 178/78, 216/253

1. What is the HCF of 178,216?

The HCF of 178,216 is 2

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 178/78, 216/253?

Answer: GCF of Numerators as per given numbers 178/78, 216/253 is

GCF of Numerators i.e. for 178,216 is 2

LCM of denominators i.e. for 78,253 is 19734.

Thus, GCF of Fractions is 2/19734.Finally, GCF of Fractions for 178/78, 216/253 is 2/19734.