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GCF of 150/25, 714/154

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 150/25, 714/154 i.e 6/3850 easily. The following is the detailed procedure to determine the greatest common factor of fractions 150/25, 714/154.

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 150/25,714/154?

Given fractions are 150/25,714/154

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 150/25,714/154, numerators are 150,714

Denominators are 25,154

The GCF of 150,714 is 6 .

LCM of 25,154 is 3850.

The greatest common factor of 150/25,714/154 = [GCF of 150,714]/[LCM of 25,154]= 6/3850

Therefore, the GCF of 150/25,714/154 is 6/3850.

Greatest Common Factor of 150,714

To find the highest common factor of 150,714, we have to find the factors of both numbers and list the highest common factor.

The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714

The HCF of 150,714 is 6.

Lets's calculate GCF of 150,714

Greatest Common Factor (GCF) of 150,714 By Common Division

2 150, 714
3 75, 357
25, 119

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 150,714 By Matching Biggest Common Factor Method

Greatest Common Factor of 150,714 By Matching Biggest Common Factor Method

Now, list down the factors of 150

:

1,2,3,5,6,10,15,25,30,50,75,150

Now, list down the factors of 714

:

1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714

Greatest Common Factor

We found the factors 150,714 . The biggest common factor number is the GCF number.
So the greatest common factor 150,714 is 6.

Lets's calculate LCM of 25,154

Lowest Common Multiple of 25,154 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3850

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/3850

Therefore, the GCF of Fractions 150/25,714/154 is 6/3850

Least Common Multiple of 25,154 with GCF Formula

Least Common Multiple of 25,154 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 25,154 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(25,154) = 1

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

GCF(25,154) x common factors =1 x 1 = 1

LCM(25,154) = ( 25 × 154 ) / 1

LCM(25,154) = 3850 / 1

LCM(25,154) = 3850


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FAQs on GCF of Fractions of 150/25, 714/154

1. What is the HCF of 150,714?

The HCF of 150,714 is 6

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 150/25, 714/154?

Answer: GCF of Numerators as per given numbers 150/25, 714/154 is

GCF of Numerators i.e. for 150,714 is 6

LCM of denominators i.e. for 25,154 is 3850.

Thus, GCF of Fractions is 6/3850.Finally, GCF of Fractions for 150/25, 714/154 is 6/3850.