How to Find GCF of 6424/138, 3596/564?

GCF of 6424/138, 3596/564

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 6424/138, 3596/564 i.e 4/12972 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6424/138, 3596/564.

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 6424/138,3596/564?

Given fractions are 6424/138,3596/564

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 6424/138,3596/564, numerators are 6424,3596

Denominators are 138,564

The GCF of 6424,3596 is 4 .

LCM of 138,564 is 12972.

The greatest common factor of 6424/138,3596/564 = [GCF of 6424,3596]/[LCM of 138,564]= 4/12972

Therefore, the GCF of 6424/138,3596/564 is 4/12972.

Greatest Common Factor of 6424,3596

To find the highest common factor of 6424,3596, we have to find the factors of both numbers and list the highest common factor.

The factors of 6424 are 1, 2, 4, 8, 11, 22, 44, 73, 88, 146, 292, 584, 803, 1606, 3212, 6424

The factors of 3596 are 1, 2, 4, 29, 31, 58, 62, 116, 124, 899, 1798, 3596

The HCF of 6424,3596 is 4.

Lets's calculate GCF of 6424,3596

Greatest Common Factor (GCF) of 6424,3596 By Common Division

2	6424, 3596
2	3212, 1798
	1606, 899

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

Greatest Common Factor of 6424,3596 By Matching Biggest Common Factor Method

Now, list down the factors of 6424

1,2,4,8,11,22,44,73,88,146,292,584,803,1606,3212,6424

Now, list down the factors of 3596

1,2,4,29,31,58,62,116,124,899,1798,3596

Greatest Common Factor

We found the factors 6424,3596 . The biggest common factor number is the GCF number.
So the greatest common factor 6424,3596 is 4.

Lets's calculate LCM of 138,564

Lowest Common Multiple of 138,564 using Common Division

2	138, 564
3	69, 282
	23, 94

∴ So the LCM of the given numbers is 2 x 3 x 23 x 94 = 12972

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/12972

Therefore, the GCF of Fractions 6424/138,3596/564 is 4/12972

Least Common Multiple of 138,564 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 138,564 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(138,564) = 6

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

GCF(138,564) x common factors =6 x 1 = 6

LCM(138,564) = ( 138 × 564 ) / 6

LCM(138,564) = 77832 / 6

LCM(138,564) = 12972

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FAQs on GCF of Fractions of 6424/138, 3596/564

1. What is the HCF of 6424,3596?

The HCF of 6424,3596 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 6424/138, 3596/564?

Answer: GCF of Numerators as per given numbers 6424/138, 3596/564 is

GCF of Numerators i.e. for 6424,3596 is 4

LCM of denominators i.e. for 138,564 is 12972.

Thus, GCF of Fractions is 4/12972.Finally, GCF of Fractions for 6424/138, 3596/564 is 4/12972.