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GCF of 2117/760, 9578/196

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 2117/760, 9578/196 i.e 1/37240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2117/760, 9578/196.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 2117/760,9578/196?

Given fractions are 2117/760,9578/196

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 2117/760,9578/196, numerators are 2117,9578

Denominators are 760,196

The GCF of 2117,9578 is 1 .

LCM of 760,196 is 37240.

The greatest common factor of 2117/760,9578/196 = [GCF of 2117,9578]/[LCM of 760,196]= 1/37240

Therefore, the GCF of 2117/760,9578/196 is 1/37240.

Greatest Common Factor of 2117,9578

To find the highest common factor of 2117,9578, we have to find the factors of both numbers and list the highest common factor.

The factors of 2117 are 1, 29, 73, 2117

The factors of 9578 are 1, 2, 4789, 9578

The HCF of 2117,9578 is 1.

Lets's calculate GCF of 2117,9578

Greatest Common Factor (GCF) of 2117,9578 By Common Division

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

Greatest Common Factor of 2117,9578 By Matching Biggest Common Factor Method

Greatest Common Factor of 2117,9578 By Matching Biggest Common Factor Method

Now, list down the factors of 2117

:

1,29,73,2117

Now, list down the factors of 9578

:

1,2,4789,9578

Greatest Common Factor

We found the factors 2117,9578 . The biggest common factor number is the GCF number.
So the greatest common factor 2117,9578 is 1.

Lets's calculate LCM of 760,196

Lowest Common Multiple of 760,196 using Common Division

2 760, 196
2 380, 98
190, 49

∴ So the LCM of the given numbers is 2 x 2 x 190 x 49 = 37240

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/37240

Therefore, the GCF of Fractions 2117/760,9578/196 is 1/37240

Least Common Multiple of 760,196 with GCF Formula

Least Common Multiple of 760,196 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 760,196 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(760,196) = 4

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

GCF(760,196) x common factors =4 x 1 = 4

LCM(760,196) = ( 760 × 196 ) / 4

LCM(760,196) = 148960 / 4

LCM(760,196) = 37240


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FAQs on GCF of Fractions of 2117/760, 9578/196

1. What is the HCF of 2117,9578?

The HCF of 2117,9578 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 2117/760, 9578/196?

Answer: GCF of Numerators as per given numbers 2117/760, 9578/196 is

GCF of Numerators i.e. for 2117,9578 is 1

LCM of denominators i.e. for 760,196 is 37240.

Thus, GCF of Fractions is 1/37240.Finally, GCF of Fractions for 2117/760, 9578/196 is 1/37240.