How to Find GCF of 624/31, 684/568?

GCF of 624/31, 684/568

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 624/31, 684/568 i.e 12/17608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 624/31, 684/568.

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 624/31,684/568?

Given fractions are 624/31,684/568

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 624/31,684/568, numerators are 624,684

Denominators are 31,568

The GCF of 624,684 is 12 .

LCM of 31,568 is 17608.

The greatest common factor of 624/31,684/568 = [GCF of 624,684]/[LCM of 31,568]= 12/17608

Therefore, the GCF of 624/31,684/568 is 12/17608.

Greatest Common Factor of 624,684

To find the highest common factor of 624,684, we have to find the factors of both numbers and list the highest common factor.

The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624

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

The HCF of 624,684 is 12.

Lets's calculate GCF of 624,684

Greatest Common Factor (GCF) of 624,684 By Common Division

2	624, 684
2	312, 342
3	156, 171
	52, 57

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 624,684 By Matching Biggest Common Factor Method

Now, list down the factors of 624

1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624

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

Greatest Common Factor

We found the factors 624,684 . The biggest common factor number is the GCF number.
So the greatest common factor 624,684 is 12.

Lets's calculate LCM of 31,568

Lowest Common Multiple of 31,568 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 17608

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/17608

Therefore, the GCF of Fractions 624/31,684/568 is 12/17608

Least Common Multiple of 31,568 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 31,568 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,568) = 1

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

GCF(31,568) x common factors =1 x 1 = 1

LCM(31,568) = ( 31 × 568 ) / 1

LCM(31,568) = 17608 / 1

LCM(31,568) = 17608

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FAQs on GCF of Fractions of 624/31, 684/568

1. What is the HCF of 624,684?

The HCF of 624,684 is 12

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 624/31, 684/568?

Answer: GCF of Numerators as per given numbers 624/31, 684/568 is

GCF of Numerators i.e. for 624,684 is 12

LCM of denominators i.e. for 31,568 is 17608.

Thus, GCF of Fractions is 12/17608.Finally, GCF of Fractions for 624/31, 684/568 is 12/17608.