How to Find GCF of 168/25, 312/8090?

GCF of 168/25, 312/8090

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 168/25, 312/8090 i.e 24/40450 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/25, 312/8090.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 168/25,312/8090?

Given fractions are 168/25,312/8090

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 168/25,312/8090, numerators are 168,312

Denominators are 25,8090

The GCF of 168,312 is 24 .

LCM of 25,8090 is 40450.

The greatest common factor of 168/25,312/8090 = [GCF of 168,312]/[LCM of 25,8090]= 24/40450

Therefore, the GCF of 168/25,312/8090 is 24/40450.

Greatest Common Factor of 168,312

To find the highest common factor of 168,312, we have to find the factors of both numbers and list the highest common factor.

The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

The HCF of 168,312 is 24.

Lets's calculate GCF of 168,312

Greatest Common Factor (GCF) of 168,312 By Common Division

2	168, 312
2	84, 156
2	42, 78
3	21, 39
	7, 13

∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24

Greatest Common Factor of 168,312 By Matching Biggest Common Factor Method

Now, list down the factors of 168

1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168

Now, list down the factors of 312

1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312

Greatest Common Factor

We found the factors 168,312 . The biggest common factor number is the GCF number.
So the greatest common factor 168,312 is 24.

Lets's calculate LCM of 25,8090

Lowest Common Multiple of 25,8090 using Common Division

5	25, 8090
	5, 1618

∴ So the LCM of the given numbers is 5 x 5 x 1618 = 40450

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/40450

Therefore, the GCF of Fractions 168/25,312/8090 is 24/40450

Least Common Multiple of 25,8090 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 25,8090 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(25,8090) = 5

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

GCF(25,8090) x common factors =5 x 1 = 5

LCM(25,8090) = ( 25 × 8090 ) / 5

LCM(25,8090) = 202250 / 5

LCM(25,8090) = 40450

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FAQs on GCF of Fractions of 168/25, 312/8090

1. What is the HCF of 168,312?

The HCF of 168,312 is 24

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 168/25, 312/8090?

Answer: GCF of Numerators as per given numbers 168/25, 312/8090 is

GCF of Numerators i.e. for 168,312 is 24

LCM of denominators i.e. for 25,8090 is 40450.

Thus, GCF of Fractions is 24/40450.Finally, GCF of Fractions for 168/25, 312/8090 is 24/40450.