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GCF of 117/12, 786/160

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 117/12, 786/160 i.e 3/480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 117/12, 786/160.

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 117/12,786/160?

Given fractions are 117/12,786/160

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 117/12,786/160, numerators are 117,786

Denominators are 12,160

The GCF of 117,786 is 3 .

LCM of 12,160 is 480.

The greatest common factor of 117/12,786/160 = [GCF of 117,786]/[LCM of 12,160]= 3/480

Therefore, the GCF of 117/12,786/160 is 3/480.

Greatest Common Factor of 117,786

To find the highest common factor of 117,786, we have to find the factors of both numbers and list the highest common factor.

The factors of 117 are 1, 3, 9, 13, 39, 117

The factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786

The HCF of 117,786 is 3.

Lets's calculate GCF of 117,786

Greatest Common Factor (GCF) of 117,786 By Common Division

3 117, 786
39, 262

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 117,786 By Matching Biggest Common Factor Method

Greatest Common Factor of 117,786 By Matching Biggest Common Factor Method

Now, list down the factors of 117

:

1,3,9,13,39,117

Now, list down the factors of 786

:

1,2,3,6,131,262,393,786

Greatest Common Factor

We found the factors 117,786 . The biggest common factor number is the GCF number.
So the greatest common factor 117,786 is 3.

Lets's calculate LCM of 12,160

Lowest Common Multiple of 12,160 using Common Division

2 12, 160
2 6, 80
3, 40

∴ So the LCM of the given numbers is 2 x 2 x 3 x 40 = 480

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/480

Therefore, the GCF of Fractions 117/12,786/160 is 3/480

Least Common Multiple of 12,160 with GCF Formula

Least Common Multiple of 12,160 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 12,160 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,160) = 4

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

GCF(12,160) x common factors =4 x 1 = 4

LCM(12,160) = ( 12 × 160 ) / 4

LCM(12,160) = 1920 / 4

LCM(12,160) = 480


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FAQs on GCF of Fractions of 117/12, 786/160

1. What is the HCF of 117,786?

The HCF of 117,786 is 3

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 117/12, 786/160?

Answer: GCF of Numerators as per given numbers 117/12, 786/160 is

GCF of Numerators i.e. for 117,786 is 3

LCM of denominators i.e. for 12,160 is 480.

Thus, GCF of Fractions is 3/480.Finally, GCF of Fractions for 117/12, 786/160 is 3/480.