How to Find GCF of 712/21, 140/9302?

GCF of 712/21, 140/9302

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 712/21, 140/9302 i.e 4/195342 easily. The following is the detailed procedure to determine the greatest common factor of fractions 712/21, 140/9302.

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 712/21,140/9302?

Given fractions are 712/21,140/9302

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 712/21,140/9302, numerators are 712,140

Denominators are 21,9302

The GCF of 712,140 is 4 .

LCM of 21,9302 is 195342.

The greatest common factor of 712/21,140/9302 = [GCF of 712,140]/[LCM of 21,9302]= 4/195342

Therefore, the GCF of 712/21,140/9302 is 4/195342.

Greatest Common Factor of 712,140

To find the highest common factor of 712,140, we have to find the factors of both numbers and list the highest common factor.

The factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712

The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140

The HCF of 712,140 is 4.

Lets's calculate GCF of 712,140

Greatest Common Factor (GCF) of 712,140 By Common Division

2	712, 140
2	356, 70
	178, 35

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

Greatest Common Factor of 712,140 By Matching Biggest Common Factor Method

Now, list down the factors of 712

1,2,4,8,89,178,356,712

Now, list down the factors of 140

1,2,4,5,7,10,14,20,28,35,70,140

Greatest Common Factor

We found the factors 712,140 . The biggest common factor number is the GCF number.
So the greatest common factor 712,140 is 4.

Lets's calculate LCM of 21,9302

Lowest Common Multiple of 21,9302 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 195342

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/195342

Therefore, the GCF of Fractions 712/21,140/9302 is 4/195342

Least Common Multiple of 21,9302 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 21,9302 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(21,9302) = 1

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

GCF(21,9302) x common factors =1 x 1 = 1

LCM(21,9302) = ( 21 × 9302 ) / 1

LCM(21,9302) = 195342 / 1

LCM(21,9302) = 195342

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 712/21, 140/9302

1. What is the HCF of 712,140?

The HCF of 712,140 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 712/21, 140/9302?

Answer: GCF of Numerators as per given numbers 712/21, 140/9302 is

GCF of Numerators i.e. for 712,140 is 4

LCM of denominators i.e. for 21,9302 is 195342.

Thus, GCF of Fractions is 4/195342.Finally, GCF of Fractions for 712/21, 140/9302 is 4/195342.