How to Find GCF of 5410/643, 5650/6138?

GCF of 5410/643, 5650/6138

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 5410/643, 5650/6138 i.e 10/3946734 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5410/643, 5650/6138.

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 5410/643,5650/6138?

Given fractions are 5410/643,5650/6138

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 5410/643,5650/6138, numerators are 5410,5650

Denominators are 643,6138

The GCF of 5410,5650 is 10 .

LCM of 643,6138 is 3946734.

The greatest common factor of 5410/643,5650/6138 = [GCF of 5410,5650]/[LCM of 643,6138]= 10/3946734

Therefore, the GCF of 5410/643,5650/6138 is 10/3946734.

Greatest Common Factor of 5410,5650

To find the highest common factor of 5410,5650, we have to find the factors of both numbers and list the highest common factor.

The factors of 5410 are 1, 2, 5, 10, 541, 1082, 2705, 5410

The factors of 5650 are 1, 2, 5, 10, 25, 50, 113, 226, 565, 1130, 2825, 5650

The HCF of 5410,5650 is 10.

Lets's calculate GCF of 5410,5650

Greatest Common Factor (GCF) of 5410,5650 By Common Division

2	5410, 5650
5	2705, 2825
	541, 565

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 5410,5650 By Matching Biggest Common Factor Method

Now, list down the factors of 5410

1,2,5,10,541,1082,2705,5410

Now, list down the factors of 5650

1,2,5,10,25,50,113,226,565,1130,2825,5650

Greatest Common Factor

We found the factors 5410,5650 . The biggest common factor number is the GCF number.
So the greatest common factor 5410,5650 is 10.

Lets's calculate LCM of 643,6138

Lowest Common Multiple of 643,6138 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3946734

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/3946734

Therefore, the GCF of Fractions 5410/643,5650/6138 is 10/3946734

Least Common Multiple of 643,6138 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 643,6138 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(643,6138) = 1

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

GCF(643,6138) x common factors =1 x 1 = 1

LCM(643,6138) = ( 643 × 6138 ) / 1

LCM(643,6138) = 3946734 / 1

LCM(643,6138) = 3946734

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FAQs on GCF of Fractions of 5410/643, 5650/6138

1. What is the HCF of 5410,5650?

The HCF of 5410,5650 is 10

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 5410/643, 5650/6138?

Answer: GCF of Numerators as per given numbers 5410/643, 5650/6138 is

GCF of Numerators i.e. for 5410,5650 is 10

LCM of denominators i.e. for 643,6138 is 3946734.

Thus, GCF of Fractions is 10/3946734.Finally, GCF of Fractions for 5410/643, 5650/6138 is 10/3946734.