How to Find GCF of 684/334, 1504/925?

GCF of 684/334, 1504/925

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 684/334, 1504/925 i.e 4/308950 easily. The following is the detailed procedure to determine the greatest common factor of fractions 684/334, 1504/925.

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 684/334,1504/925?

Given fractions are 684/334,1504/925

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 684/334,1504/925, numerators are 684,1504

Denominators are 334,925

The GCF of 684,1504 is 4 .

LCM of 334,925 is 308950.

The greatest common factor of 684/334,1504/925 = [GCF of 684,1504]/[LCM of 334,925]= 4/308950

Therefore, the GCF of 684/334,1504/925 is 4/308950.

Greatest Common Factor of 684,1504

To find the highest common factor of 684,1504, we have to find the factors of both numbers and list the highest common factor.

The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684

The factors of 1504 are 1, 2, 4, 8, 16, 32, 47, 94, 188, 376, 752, 1504

The HCF of 684,1504 is 4.

Lets's calculate GCF of 684,1504

Greatest Common Factor (GCF) of 684,1504 By Common Division

2	684, 1504
2	342, 752
	171, 376

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 684,1504 By Matching Biggest Common Factor Method

Now, list down the factors of 684

1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684

Now, list down the factors of 1504

1,2,4,8,16,32,47,94,188,376,752,1504

Greatest Common Factor

We found the factors 684,1504 . The biggest common factor number is the GCF number.
So the greatest common factor 684,1504 is 4.

Lets's calculate LCM of 334,925

Lowest Common Multiple of 334,925 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 308950

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/308950

Therefore, the GCF of Fractions 684/334,1504/925 is 4/308950

Least Common Multiple of 334,925 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 334,925 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(334,925) = 1

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

GCF(334,925) x common factors =1 x 1 = 1

LCM(334,925) = ( 334 × 925 ) / 1

LCM(334,925) = 308950 / 1

LCM(334,925) = 308950

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FAQs on GCF of Fractions of 684/334, 1504/925

1. What is the HCF of 684,1504?

The HCF of 684,1504 is 4

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 684/334, 1504/925?

Answer: GCF of Numerators as per given numbers 684/334, 1504/925 is

GCF of Numerators i.e. for 684,1504 is 4

LCM of denominators i.e. for 334,925 is 308950.

Thus, GCF of Fractions is 4/308950.Finally, GCF of Fractions for 684/334, 1504/925 is 4/308950.