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GCF of 152/218, 654/689

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 152/218, 654/689 i.e 2/150202 easily. The following is the detailed procedure to determine the greatest common factor of fractions 152/218, 654/689.

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 152/218,654/689?

Given fractions are 152/218,654/689

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 152/218,654/689, numerators are 152,654

Denominators are 218,689

The GCF of 152,654 is 2 .

LCM of 218,689 is 150202.

The greatest common factor of 152/218,654/689 = [GCF of 152,654]/[LCM of 218,689]= 2/150202

Therefore, the GCF of 152/218,654/689 is 2/150202.

Greatest Common Factor of 152,654

To find the highest common factor of 152,654, we have to find the factors of both numbers and list the highest common factor.

The factors of 152 are 1, 2, 4, 8, 19, 38, 76, 152

The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654

The HCF of 152,654 is 2.

Lets's calculate GCF of 152,654

Greatest Common Factor (GCF) of 152,654 By Common Division

2 152, 654
76, 327

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

Greatest Common Factor of 152,654 By Matching Biggest Common Factor Method

Greatest Common Factor of 152,654 By Matching Biggest Common Factor Method

Now, list down the factors of 152

:

1,2,4,8,19,38,76,152

Now, list down the factors of 654

:

1,2,3,6,109,218,327,654

Greatest Common Factor

We found the factors 152,654 . The biggest common factor number is the GCF number.
So the greatest common factor 152,654 is 2.

Lets's calculate LCM of 218,689

Lowest Common Multiple of 218,689 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 150202

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/150202

Therefore, the GCF of Fractions 152/218,654/689 is 2/150202

Least Common Multiple of 218,689 with GCF Formula

Least Common Multiple of 218,689 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 218,689 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(218,689) = 1

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

GCF(218,689) x common factors =1 x 1 = 1

LCM(218,689) = ( 218 × 689 ) / 1

LCM(218,689) = 150202 / 1

LCM(218,689) = 150202


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FAQs on GCF of Fractions of 152/218, 654/689

1. What is the HCF of 152,654?

The HCF of 152,654 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 152/218, 654/689?

Answer: GCF of Numerators as per given numbers 152/218, 654/689 is

GCF of Numerators i.e. for 152,654 is 2

LCM of denominators i.e. for 218,689 is 150202.

Thus, GCF of Fractions is 2/150202.Finally, GCF of Fractions for 152/218, 654/689 is 2/150202.