How to Find GCF of 84/62, 109/45, 653/744?

GCF of 84/62, 109/45, 653/744

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 84/62, 109/45, 653/744 i.e 1/11160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 84/62, 109/45, 653/744.

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 84/62,109/45,653/744?

Given fractions are 84/62,109/45,653/744

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 84/62,109/45,653/744, numerators are 84,109,653

Denominators are 62,45,744

The GCF of 84,109,653 is 1 .

LCM of 62,45,744 is 11160.

The greatest common factor of 84/62,109/45,653/744 = [GCF of 84,109,653]/[LCM of 62,45,744]= 1/11160

Therefore, the GCF of 84/62,109/45,653/744 is 1/11160.

Greatest Common Factor of 84,109,653

To find the highest common factor of 84,109,653, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 109 are 1, 109

The factors of 653 are 1, 653

The HCF of 84,109,653 is 1.

Lets's calculate GCF of 84,109,653

Greatest Common Factor (GCF) of 84,109,653 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 84,109,653 By Matching Biggest Common Factor Method

Now, list down the factors of 84

1,2,3,4,6,7,12,14,21,28,42,84

Now, list down the factors of 109

1,109

Now, list down the factors of 653

1,653

Greatest Common Factor

We found the factors 84,109,653 . The biggest common factor number is the GCF number.
So the greatest common factor 84,109,653 is 1.

Lets's calculate LCM of 62,45,744

Lowest Common Multiple of 62,45,744 using Common Division

2	62, 45, 744
3	31, 45, 372
31	31, 15, 124
	1, 15, 4

∴ So the LCM of the given numbers is 2 x 3 x 31 x 1 x 15 x 4 = 11160

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11160

Therefore, the GCF of Fractions 84/62,109/45,653/744 is 1/11160

Least Common Multiple of 62,45,744 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 62,45,744 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(62,45,744) = 1

common factors(in case of two or more numbers have common factors) = 186

GCF(62,45,744) x common factors =1 x 186 = 186

LCM(62,45,744) = ( 62 × 45 × 744 ) / 186

LCM(62,45,744) = 2075760 / 186

LCM(62,45,744) = 11160

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 84/62, 109/45, 653/744

1. What is the HCF of 84,109,653?

The HCF of 84,109,653 is 1

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 84/62, 109/45, 653/744?

Answer: GCF of Numerators as per given numbers 84/62, 109/45, 653/744 is

GCF of Numerators i.e. for 84,109,653 is 1

LCM of denominators i.e. for 62,45,744 is 11160.

Thus, GCF of Fractions is 1/11160.Finally, GCF of Fractions for 84/62, 109/45, 653/744 is 1/11160.