How to Find GCF of 916/78, 588/1718?

GCF of 916/78, 588/1718

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 916/78, 588/1718 i.e 4/67002 easily. The following is the detailed procedure to determine the greatest common factor of fractions 916/78, 588/1718.

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 916/78,588/1718?

Given fractions are 916/78,588/1718

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 916/78,588/1718, numerators are 916,588

Denominators are 78,1718

The GCF of 916,588 is 4 .

LCM of 78,1718 is 67002.

The greatest common factor of 916/78,588/1718 = [GCF of 916,588]/[LCM of 78,1718]= 4/67002

Therefore, the GCF of 916/78,588/1718 is 4/67002.

Greatest Common Factor of 916,588

To find the highest common factor of 916,588, we have to find the factors of both numbers and list the highest common factor.

The factors of 916 are 1, 2, 4, 229, 458, 916

The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588

The HCF of 916,588 is 4.

Lets's calculate GCF of 916,588

Greatest Common Factor (GCF) of 916,588 By Common Division

2	916, 588
2	458, 294
	229, 147

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 916,588 By Matching Biggest Common Factor Method

Now, list down the factors of 916

1,2,4,229,458,916

Now, list down the factors of 588

1,2,3,4,6,7,12,14,21,28,42,49,84,98,147,196,294,588

Greatest Common Factor

We found the factors 916,588 . The biggest common factor number is the GCF number.
So the greatest common factor 916,588 is 4.

Lets's calculate LCM of 78,1718

Lowest Common Multiple of 78,1718 using Common Division

2	78, 1718
	39, 859

∴ So the LCM of the given numbers is 2 x 39 x 859 = 67002

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/67002

Therefore, the GCF of Fractions 916/78,588/1718 is 4/67002

Least Common Multiple of 78,1718 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 78,1718 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,1718) = 2

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

GCF(78,1718) x common factors =2 x 1 = 2

LCM(78,1718) = ( 78 × 1718 ) / 2

LCM(78,1718) = 134004 / 2

LCM(78,1718) = 67002

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FAQs on GCF of Fractions of 916/78, 588/1718

1. What is the HCF of 916,588?

The HCF of 916,588 is 4

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 916/78, 588/1718?

Answer: GCF of Numerators as per given numbers 916/78, 588/1718 is

GCF of Numerators i.e. for 916,588 is 4

LCM of denominators i.e. for 78,1718 is 67002.

Thus, GCF of Fractions is 4/67002.Finally, GCF of Fractions for 916/78, 588/1718 is 4/67002.