How to Find GCF of 7122/152, 7887/1924?

GCF of 7122/152, 7887/1924

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 7122/152, 7887/1924 i.e 3/73112 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7122/152, 7887/1924.

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 7122/152,7887/1924?

Given fractions are 7122/152,7887/1924

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 7122/152,7887/1924, numerators are 7122,7887

Denominators are 152,1924

The GCF of 7122,7887 is 3 .

LCM of 152,1924 is 73112.

The greatest common factor of 7122/152,7887/1924 = [GCF of 7122,7887]/[LCM of 152,1924]= 3/73112

Therefore, the GCF of 7122/152,7887/1924 is 3/73112.

Greatest Common Factor of 7122,7887

To find the highest common factor of 7122,7887, we have to find the factors of both numbers and list the highest common factor.

The factors of 7122 are 1, 2, 3, 6, 1187, 2374, 3561, 7122

The factors of 7887 are 1, 3, 11, 33, 239, 717, 2629, 7887

The HCF of 7122,7887 is 3.

Lets's calculate GCF of 7122,7887

Greatest Common Factor (GCF) of 7122,7887 By Common Division

3	7122, 7887
	2374, 2629

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

Greatest Common Factor of 7122,7887 By Matching Biggest Common Factor Method

Now, list down the factors of 7122

1,2,3,6,1187,2374,3561,7122

Now, list down the factors of 7887

1,3,11,33,239,717,2629,7887

Greatest Common Factor

We found the factors 7122,7887 . The biggest common factor number is the GCF number.
So the greatest common factor 7122,7887 is 3.

Lets's calculate LCM of 152,1924

Lowest Common Multiple of 152,1924 using Common Division

2	152, 1924
2	76, 962
	38, 481

∴ So the LCM of the given numbers is 2 x 2 x 38 x 481 = 73112

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/73112

Therefore, the GCF of Fractions 7122/152,7887/1924 is 3/73112

Least Common Multiple of 152,1924 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 152,1924 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(152,1924) = 4

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

GCF(152,1924) x common factors =4 x 1 = 4

LCM(152,1924) = ( 152 × 1924 ) / 4

LCM(152,1924) = 292448 / 4

LCM(152,1924) = 73112

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FAQs on GCF of Fractions of 7122/152, 7887/1924

1. What is the HCF of 7122,7887?

The HCF of 7122,7887 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 7122/152, 7887/1924?

Answer: GCF of Numerators as per given numbers 7122/152, 7887/1924 is

GCF of Numerators i.e. for 7122,7887 is 3

LCM of denominators i.e. for 152,1924 is 73112.

Thus, GCF of Fractions is 3/73112.Finally, GCF of Fractions for 7122/152, 7887/1924 is 3/73112.