How to Find GCF of 974/661, 3042/686?

GCF of 974/661, 3042/686

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 974/661, 3042/686 i.e 2/453446 easily. The following is the detailed procedure to determine the greatest common factor of fractions 974/661, 3042/686.

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 974/661,3042/686?

Given fractions are 974/661,3042/686

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 974/661,3042/686, numerators are 974,3042

Denominators are 661,686

The GCF of 974,3042 is 2 .

LCM of 661,686 is 453446.

The greatest common factor of 974/661,3042/686 = [GCF of 974,3042]/[LCM of 661,686]= 2/453446

Therefore, the GCF of 974/661,3042/686 is 2/453446.

Greatest Common Factor of 974,3042

To find the highest common factor of 974,3042, we have to find the factors of both numbers and list the highest common factor.

The factors of 974 are 1, 2, 487, 974

The factors of 3042 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 169, 234, 338, 507, 1014, 1521, 3042

The HCF of 974,3042 is 2.

Lets's calculate GCF of 974,3042

Greatest Common Factor (GCF) of 974,3042 By Common Division

2	974, 3042
	487, 1521

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

Greatest Common Factor of 974,3042 By Matching Biggest Common Factor Method

Now, list down the factors of 974

1,2,487,974

Now, list down the factors of 3042

1,2,3,6,9,13,18,26,39,78,117,169,234,338,507,1014,1521,3042

Greatest Common Factor

We found the factors 974,3042 . The biggest common factor number is the GCF number.
So the greatest common factor 974,3042 is 2.

Lets's calculate LCM of 661,686

Lowest Common Multiple of 661,686 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 453446

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/453446

Therefore, the GCF of Fractions 974/661,3042/686 is 2/453446

Least Common Multiple of 661,686 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 661,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(661,686) = 1

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

GCF(661,686) x common factors =1 x 1 = 1

LCM(661,686) = ( 661 × 686 ) / 1

LCM(661,686) = 453446 / 1

LCM(661,686) = 453446

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FAQs on GCF of Fractions of 974/661, 3042/686

1. What is the HCF of 974,3042?

The HCF of 974,3042 is 2

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 974/661, 3042/686?

Answer: GCF of Numerators as per given numbers 974/661, 3042/686 is

GCF of Numerators i.e. for 974,3042 is 2

LCM of denominators i.e. for 661,686 is 453446.

Thus, GCF of Fractions is 2/453446.Finally, GCF of Fractions for 974/661, 3042/686 is 2/453446.