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GCF of 753/54, 312/661

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 753/54, 312/661 i.e 3/35694 easily. The following is the detailed procedure to determine the greatest common factor of fractions 753/54, 312/661.

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 753/54,312/661?

Given fractions are 753/54,312/661

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 753/54,312/661, numerators are 753,312

Denominators are 54,661

The GCF of 753,312 is 3 .

LCM of 54,661 is 35694.

The greatest common factor of 753/54,312/661 = [GCF of 753,312]/[LCM of 54,661]= 3/35694

Therefore, the GCF of 753/54,312/661 is 3/35694.

Greatest Common Factor of 753,312

To find the highest common factor of 753,312, we have to find the factors of both numbers and list the highest common factor.

The factors of 753 are 1, 3, 251, 753

The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

The HCF of 753,312 is 3.

Lets's calculate GCF of 753,312

Greatest Common Factor (GCF) of 753,312 By Common Division

3 753, 312
251, 104

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 753,312 By Matching Biggest Common Factor Method

Greatest Common Factor of 753,312 By Matching Biggest Common Factor Method

Now, list down the factors of 753

:

1,3,251,753

Now, list down the factors of 312

:

1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312

Greatest Common Factor

We found the factors 753,312 . The biggest common factor number is the GCF number.
So the greatest common factor 753,312 is 3.

Lets's calculate LCM of 54,661

Lowest Common Multiple of 54,661 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 35694

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/35694

Therefore, the GCF of Fractions 753/54,312/661 is 3/35694

Least Common Multiple of 54,661 with GCF Formula

Least Common Multiple of 54,661 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 54,661 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(54,661) = 1

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

GCF(54,661) x common factors =1 x 1 = 1

LCM(54,661) = ( 54 × 661 ) / 1

LCM(54,661) = 35694 / 1

LCM(54,661) = 35694


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FAQs on GCF of Fractions of 753/54, 312/661

1. What is the HCF of 753,312?

The HCF of 753,312 is 3

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 753/54, 312/661?

Answer: GCF of Numerators as per given numbers 753/54, 312/661 is

GCF of Numerators i.e. for 753,312 is 3

LCM of denominators i.e. for 54,661 is 35694.

Thus, GCF of Fractions is 3/35694.Finally, GCF of Fractions for 753/54, 312/661 is 3/35694.