How to Find GCF of 5478/972, 7507/132?

GCF of 5478/972, 7507/132

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 5478/972, 7507/132 i.e 1/10692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5478/972, 7507/132.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 5478/972,7507/132?

Given fractions are 5478/972,7507/132

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 5478/972,7507/132, numerators are 5478,7507

Denominators are 972,132

The GCF of 5478,7507 is 1 .

LCM of 972,132 is 10692.

The greatest common factor of 5478/972,7507/132 = [GCF of 5478,7507]/[LCM of 972,132]= 1/10692

Therefore, the GCF of 5478/972,7507/132 is 1/10692.

Greatest Common Factor of 5478,7507

To find the highest common factor of 5478,7507, we have to find the factors of both numbers and list the highest common factor.

The factors of 5478 are 1, 2, 3, 6, 11, 22, 33, 66, 83, 166, 249, 498, 913, 1826, 2739, 5478

The factors of 7507 are 1, 7507

The HCF of 5478,7507 is 1.

Lets's calculate GCF of 5478,7507

Greatest Common Factor (GCF) of 5478,7507 By Common Division

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

Greatest Common Factor of 5478,7507 By Matching Biggest Common Factor Method

Now, list down the factors of 5478

1,2,3,6,11,22,33,66,83,166,249,498,913,1826,2739,5478

Now, list down the factors of 7507

1,7507

Greatest Common Factor

We found the factors 5478,7507 . The biggest common factor number is the GCF number.
So the greatest common factor 5478,7507 is 1.

Lets's calculate LCM of 972,132

Lowest Common Multiple of 972,132 using Common Division

2	972, 132
2	486, 66
3	243, 33
	81, 11

∴ So the LCM of the given numbers is 2 x 2 x 3 x 81 x 11 = 10692

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10692

Therefore, the GCF of Fractions 5478/972,7507/132 is 1/10692

Least Common Multiple of 972,132 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 972,132 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(972,132) = 12

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

GCF(972,132) x common factors =12 x 1 = 12

LCM(972,132) = ( 972 × 132 ) / 12

LCM(972,132) = 128304 / 12

LCM(972,132) = 10692

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FAQs on GCF of Fractions of 5478/972, 7507/132

1. What is the HCF of 5478,7507?

The HCF of 5478,7507 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 5478/972, 7507/132?

Answer: GCF of Numerators as per given numbers 5478/972, 7507/132 is

GCF of Numerators i.e. for 5478,7507 is 1

LCM of denominators i.e. for 972,132 is 10692.

Thus, GCF of Fractions is 1/10692.Finally, GCF of Fractions for 5478/972, 7507/132 is 1/10692.