How to Find GCF of 74/723, 86/674, 142/420?

GCF of 74/723, 86/674, 142/420

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 74/723, 86/674, 142/420 i.e 2/34111140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 74/723, 86/674, 142/420.

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 74/723,86/674,142/420?

Given fractions are 74/723,86/674,142/420

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 74/723,86/674,142/420, numerators are 74,86,142

Denominators are 723,674,420

The GCF of 74,86,142 is 2 .

LCM of 723,674,420 is 34111140.

The greatest common factor of 74/723,86/674,142/420 = [GCF of 74,86,142]/[LCM of 723,674,420]= 2/34111140

Therefore, the GCF of 74/723,86/674,142/420 is 2/34111140.

Greatest Common Factor of 74,86,142

To find the highest common factor of 74,86,142, we have to find the factors of both numbers and list the highest common factor.

The factors of 74 are 1, 2, 37, 74

The factors of 86 are 1, 2, 43, 86

The factors of 142 are 1, 2, 71, 142

The HCF of 74,86,142 is 2.

Lets's calculate GCF of 74,86,142

Greatest Common Factor (GCF) of 74,86,142 By Common Division

2	74, 86, 142
	37, 43, 71

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

Greatest Common Factor of 74,86,142 By Matching Biggest Common Factor Method

Now, list down the factors of 74

1,2,37,74

Now, list down the factors of 86

1,2,43,86

Now, list down the factors of 142

1,2,71,142

Greatest Common Factor

We found the factors 74,86,142 . The biggest common factor number is the GCF number.
So the greatest common factor 74,86,142 is 2.

Lets's calculate LCM of 723,674,420

Lowest Common Multiple of 723,674,420 using Common Division

2	723, 674, 420
3	723, 337, 210
	241, 337, 70

∴ So the LCM of the given numbers is 2 x 3 x 241 x 337 x 70 = 34111140

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/34111140

Therefore, the GCF of Fractions 74/723,86/674,142/420 is 2/34111140

Least Common Multiple of 723,674,420 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 723,674,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(723,674,420) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(723,674,420) x common factors =1 x 6 = 6

LCM(723,674,420) = ( 723 × 674 × 420 ) / 6

LCM(723,674,420) = 204666840 / 6

LCM(723,674,420) = 34111140

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 74/723, 86/674, 142/420

1. What is the HCF of 74,86,142?

The HCF of 74,86,142 is 2

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 74/723, 86/674, 142/420?

Answer: GCF of Numerators as per given numbers 74/723, 86/674, 142/420 is

GCF of Numerators i.e. for 74,86,142 is 2

LCM of denominators i.e. for 723,674,420 is 34111140.

Thus, GCF of Fractions is 2/34111140.Finally, GCF of Fractions for 74/723, 86/674, 142/420 is 2/34111140.