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GCF of 120/85, 808/5678

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 120/85, 808/5678 i.e 8/28390 easily. The following is the detailed procedure to determine the greatest common factor of fractions 120/85, 808/5678.

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 120/85,808/5678?

Given fractions are 120/85,808/5678

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 120/85,808/5678, numerators are 120,808

Denominators are 85,5678

The GCF of 120,808 is 8 .

LCM of 85,5678 is 28390.

The greatest common factor of 120/85,808/5678 = [GCF of 120,808]/[LCM of 85,5678]= 8/28390

Therefore, the GCF of 120/85,808/5678 is 8/28390.

Greatest Common Factor of 120,808

To find the highest common factor of 120,808, we have to find the factors of both numbers and list the highest common factor.

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The factors of 808 are 1, 2, 4, 8, 101, 202, 404, 808

The HCF of 120,808 is 8.

Lets's calculate GCF of 120,808

Greatest Common Factor (GCF) of 120,808 By Common Division

2 120, 808
2 60, 404
2 30, 202
15, 101

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 120,808 By Matching Biggest Common Factor Method

Greatest Common Factor of 120,808 By Matching Biggest Common Factor Method

Now, list down the factors of 120

:

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Now, list down the factors of 808

:

1,2,4,8,101,202,404,808

Greatest Common Factor

We found the factors 120,808 . The biggest common factor number is the GCF number.
So the greatest common factor 120,808 is 8.

Lets's calculate LCM of 85,5678

Lowest Common Multiple of 85,5678 using Common Division

17 85, 5678
5, 334

∴ So the LCM of the given numbers is 17 x 5 x 334 = 28390

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/28390

Therefore, the GCF of Fractions 120/85,808/5678 is 8/28390

Least Common Multiple of 85,5678 with GCF Formula

Least Common Multiple of 85,5678 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 85,5678 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(85,5678) = 17

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

GCF(85,5678) x common factors =17 x 1 = 17

LCM(85,5678) = ( 85 × 5678 ) / 17

LCM(85,5678) = 482630 / 17

LCM(85,5678) = 28390


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FAQs on GCF of Fractions of 120/85, 808/5678

1. What is the HCF of 120,808?

The HCF of 120,808 is 8

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 120/85, 808/5678?

Answer: GCF of Numerators as per given numbers 120/85, 808/5678 is

GCF of Numerators i.e. for 120,808 is 8

LCM of denominators i.e. for 85,5678 is 28390.

Thus, GCF of Fractions is 8/28390.Finally, GCF of Fractions for 120/85, 808/5678 is 8/28390.