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GCF of 758/40, 654/461

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 758/40, 654/461 i.e 2/18440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 758/40, 654/461.

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 758/40,654/461?

Given fractions are 758/40,654/461

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 758/40,654/461, numerators are 758,654

Denominators are 40,461

The GCF of 758,654 is 2 .

LCM of 40,461 is 18440.

The greatest common factor of 758/40,654/461 = [GCF of 758,654]/[LCM of 40,461]= 2/18440

Therefore, the GCF of 758/40,654/461 is 2/18440.

Greatest Common Factor of 758,654

To find the highest common factor of 758,654, we have to find the factors of both numbers and list the highest common factor.

The factors of 758 are 1, 2, 379, 758

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

The HCF of 758,654 is 2.

Lets's calculate GCF of 758,654

Greatest Common Factor (GCF) of 758,654 By Common Division

2 758, 654
379, 327

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

Greatest Common Factor of 758,654 By Matching Biggest Common Factor Method

Greatest Common Factor of 758,654 By Matching Biggest Common Factor Method

Now, list down the factors of 758

:

1,2,379,758

Now, list down the factors of 654

:

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

Greatest Common Factor

We found the factors 758,654 . The biggest common factor number is the GCF number.
So the greatest common factor 758,654 is 2.

Lets's calculate LCM of 40,461

Lowest Common Multiple of 40,461 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 18440

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/18440

Therefore, the GCF of Fractions 758/40,654/461 is 2/18440

Least Common Multiple of 40,461 with GCF Formula

Least Common Multiple of 40,461 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 40,461 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,461) = 1

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

GCF(40,461) x common factors =1 x 1 = 1

LCM(40,461) = ( 40 × 461 ) / 1

LCM(40,461) = 18440 / 1

LCM(40,461) = 18440


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FAQs on GCF of Fractions of 758/40, 654/461

1. What is the HCF of 758,654?

The HCF of 758,654 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 758/40, 654/461?

Answer: GCF of Numerators as per given numbers 758/40, 654/461 is

GCF of Numerators i.e. for 758,654 is 2

LCM of denominators i.e. for 40,461 is 18440.

Thus, GCF of Fractions is 2/18440.Finally, GCF of Fractions for 758/40, 654/461 is 2/18440.