How to Find GCF of 970/756, 749/460?

GCF of 970/756, 749/460

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 970/756, 749/460 i.e 1/86940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 970/756, 749/460.

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 970/756,749/460?

Given fractions are 970/756,749/460

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 970/756,749/460, numerators are 970,749

Denominators are 756,460

The GCF of 970,749 is 1 .

LCM of 756,460 is 86940.

The greatest common factor of 970/756,749/460 = [GCF of 970,749]/[LCM of 756,460]= 1/86940

Therefore, the GCF of 970/756,749/460 is 1/86940.

Greatest Common Factor of 970,749

To find the highest common factor of 970,749, we have to find the factors of both numbers and list the highest common factor.

The factors of 970 are 1, 2, 5, 10, 97, 194, 485, 970

The factors of 749 are 1, 7, 107, 749

The HCF of 970,749 is 1.

Lets's calculate GCF of 970,749

Greatest Common Factor (GCF) of 970,749 By Common Division

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

Greatest Common Factor of 970,749 By Matching Biggest Common Factor Method

Now, list down the factors of 970

1,2,5,10,97,194,485,970

Now, list down the factors of 749

1,7,107,749

Greatest Common Factor

We found the factors 970,749 . The biggest common factor number is the GCF number.
So the greatest common factor 970,749 is 1.

Lets's calculate LCM of 756,460

Lowest Common Multiple of 756,460 using Common Division

2	756, 460
2	378, 230
	189, 115

∴ So the LCM of the given numbers is 2 x 2 x 189 x 115 = 86940

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/86940

Therefore, the GCF of Fractions 970/756,749/460 is 1/86940

Least Common Multiple of 756,460 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 756,460 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(756,460) = 4

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

GCF(756,460) x common factors =4 x 1 = 4

LCM(756,460) = ( 756 × 460 ) / 4

LCM(756,460) = 347760 / 4

LCM(756,460) = 86940

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FAQs on GCF of Fractions of 970/756, 749/460

1. What is the HCF of 970,749?

The HCF of 970,749 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 970/756, 749/460?

Answer: GCF of Numerators as per given numbers 970/756, 749/460 is

GCF of Numerators i.e. for 970,749 is 1

LCM of denominators i.e. for 756,460 is 86940.

Thus, GCF of Fractions is 1/86940.Finally, GCF of Fractions for 970/756, 749/460 is 1/86940.