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GCF of 975/46, 380/208

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 975/46, 380/208 i.e 5/4784 easily. The following is the detailed procedure to determine the greatest common factor of fractions 975/46, 380/208.

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 975/46,380/208?

Given fractions are 975/46,380/208

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 975/46,380/208, numerators are 975,380

Denominators are 46,208

The GCF of 975,380 is 5 .

LCM of 46,208 is 4784.

The greatest common factor of 975/46,380/208 = [GCF of 975,380]/[LCM of 46,208]= 5/4784

Therefore, the GCF of 975/46,380/208 is 5/4784.

Greatest Common Factor of 975,380

To find the highest common factor of 975,380, we have to find the factors of both numbers and list the highest common factor.

The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975

The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380

The HCF of 975,380 is 5.

Lets's calculate GCF of 975,380

Greatest Common Factor (GCF) of 975,380 By Common Division

5 975, 380
195, 76

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 975,380 By Matching Biggest Common Factor Method

Greatest Common Factor of 975,380 By Matching Biggest Common Factor Method

Now, list down the factors of 975

:

1,3,5,13,15,25,39,65,75,195,325,975

Now, list down the factors of 380

:

1,2,4,5,10,19,20,38,76,95,190,380

Greatest Common Factor

We found the factors 975,380 . The biggest common factor number is the GCF number.
So the greatest common factor 975,380 is 5.

Lets's calculate LCM of 46,208

Lowest Common Multiple of 46,208 using Common Division

2 46, 208
23, 104

∴ So the LCM of the given numbers is 2 x 23 x 104 = 4784

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/4784

Therefore, the GCF of Fractions 975/46,380/208 is 5/4784

Least Common Multiple of 46,208 with GCF Formula

Least Common Multiple of 46,208 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 46,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(46,208) = 2

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

GCF(46,208) x common factors =2 x 1 = 2

LCM(46,208) = ( 46 × 208 ) / 2

LCM(46,208) = 9568 / 2

LCM(46,208) = 4784


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FAQs on GCF of Fractions of 975/46, 380/208

1. What is the HCF of 975,380?

The HCF of 975,380 is 5

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 975/46, 380/208?

Answer: GCF of Numerators as per given numbers 975/46, 380/208 is

GCF of Numerators i.e. for 975,380 is 5

LCM of denominators i.e. for 46,208 is 4784.

Thus, GCF of Fractions is 5/4784.Finally, GCF of Fractions for 975/46, 380/208 is 5/4784.