How to Find GCF of 969/51, 980/8140?

GCF of 969/51, 980/8140

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 969/51, 980/8140 i.e 1/415140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 969/51, 980/8140.

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 969/51,980/8140?

Given fractions are 969/51,980/8140

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 969/51,980/8140, numerators are 969,980

Denominators are 51,8140

The GCF of 969,980 is 1 .

LCM of 51,8140 is 415140.

The greatest common factor of 969/51,980/8140 = [GCF of 969,980]/[LCM of 51,8140]= 1/415140

Therefore, the GCF of 969/51,980/8140 is 1/415140.

Greatest Common Factor of 969,980

To find the highest common factor of 969,980, we have to find the factors of both numbers and list the highest common factor.

The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969

The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980

The HCF of 969,980 is 1.

Lets's calculate GCF of 969,980

Greatest Common Factor (GCF) of 969,980 By Common Division

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

Greatest Common Factor of 969,980 By Matching Biggest Common Factor Method

Now, list down the factors of 969

1,3,17,19,51,57,323,969

Now, list down the factors of 980

1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980

Greatest Common Factor

We found the factors 969,980 . The biggest common factor number is the GCF number.
So the greatest common factor 969,980 is 1.

Lets's calculate LCM of 51,8140

Lowest Common Multiple of 51,8140 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 415140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/415140

Therefore, the GCF of Fractions 969/51,980/8140 is 1/415140

Least Common Multiple of 51,8140 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 51,8140 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(51,8140) = 1

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

GCF(51,8140) x common factors =1 x 1 = 1

LCM(51,8140) = ( 51 × 8140 ) / 1

LCM(51,8140) = 415140 / 1

LCM(51,8140) = 415140

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FAQs on GCF of Fractions of 969/51, 980/8140

1. What is the HCF of 969,980?

The HCF of 969,980 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 969/51, 980/8140?

Answer: GCF of Numerators as per given numbers 969/51, 980/8140 is

GCF of Numerators i.e. for 969,980 is 1

LCM of denominators i.e. for 51,8140 is 415140.

Thus, GCF of Fractions is 1/415140.Finally, GCF of Fractions for 969/51, 980/8140 is 1/415140.