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GCF of 107/24, 398/780

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 107/24, 398/780 i.e 1/1560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 107/24, 398/780.

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 107/24,398/780?

Given fractions are 107/24,398/780

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 107/24,398/780, numerators are 107,398

Denominators are 24,780

The GCF of 107,398 is 1 .

LCM of 24,780 is 1560.

The greatest common factor of 107/24,398/780 = [GCF of 107,398]/[LCM of 24,780]= 1/1560

Therefore, the GCF of 107/24,398/780 is 1/1560.

Greatest Common Factor of 107,398

To find the highest common factor of 107,398, we have to find the factors of both numbers and list the highest common factor.

The factors of 107 are 1, 107

The factors of 398 are 1, 2, 199, 398

The HCF of 107,398 is 1.

Lets's calculate GCF of 107,398

Greatest Common Factor (GCF) of 107,398 By Common Division

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

Greatest Common Factor of 107,398 By Matching Biggest Common Factor Method

Greatest Common Factor of 107,398 By Matching Biggest Common Factor Method

Now, list down the factors of 107

:

1,107

Now, list down the factors of 398

:

1,2,199,398

Greatest Common Factor

We found the factors 107,398 . The biggest common factor number is the GCF number.
So the greatest common factor 107,398 is 1.

Lets's calculate LCM of 24,780

Lowest Common Multiple of 24,780 using Common Division

2 24, 780
2 12, 390
3 6, 195
2, 65

∴ So the LCM of the given numbers is 2 x 2 x 3 x 2 x 65 = 1560

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1560

Therefore, the GCF of Fractions 107/24,398/780 is 1/1560

Least Common Multiple of 24,780 with GCF Formula

Least Common Multiple of 24,780 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 24,780 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(24,780) = 12

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

GCF(24,780) x common factors =12 x 1 = 12

LCM(24,780) = ( 24 × 780 ) / 12

LCM(24,780) = 18720 / 12

LCM(24,780) = 1560


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FAQs on GCF of Fractions of 107/24, 398/780

1. What is the HCF of 107,398?

The HCF of 107,398 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 107/24, 398/780?

Answer: GCF of Numerators as per given numbers 107/24, 398/780 is

GCF of Numerators i.e. for 107,398 is 1

LCM of denominators i.e. for 24,780 is 1560.

Thus, GCF of Fractions is 1/1560.Finally, GCF of Fractions for 107/24, 398/780 is 1/1560.