How to Find GCF of 71/84, 89/870, 101/144?

GCF of 71/84, 89/870, 101/144

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 71/84, 89/870, 101/144 i.e 1/146160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/84, 89/870, 101/144.

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 71/84,89/870,101/144?

Given fractions are 71/84,89/870,101/144

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 71/84,89/870,101/144, numerators are 71,89,101

Denominators are 84,870,144

The GCF of 71,89,101 is 1 .

LCM of 84,870,144 is 146160.

The greatest common factor of 71/84,89/870,101/144 = [GCF of 71,89,101]/[LCM of 84,870,144]= 1/146160

Therefore, the GCF of 71/84,89/870,101/144 is 1/146160.

Greatest Common Factor of 71,89,101

To find the highest common factor of 71,89,101, we have to find the factors of both numbers and list the highest common factor.

The factors of 71 are 1, 71

The factors of 89 are 1, 89

The factors of 101 are 1, 101

The HCF of 71,89,101 is 1.

Lets's calculate GCF of 71,89,101

Greatest Common Factor (GCF) of 71,89,101 By Common Division

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

Greatest Common Factor of 71,89,101 By Matching Biggest Common Factor Method

Now, list down the factors of 71

1,71

Now, list down the factors of 89

1,89

Now, list down the factors of 101

1,101

Greatest Common Factor

We found the factors 71,89,101 . The biggest common factor number is the GCF number.
So the greatest common factor 71,89,101 is 1.

Lets's calculate LCM of 84,870,144

Lowest Common Multiple of 84,870,144 using Common Division

2	84, 870, 144
2	42, 435, 72
3	21, 435, 36
	7, 145, 12

∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 145 x 12 = 146160

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/146160

Therefore, the GCF of Fractions 71/84,89/870,101/144 is 1/146160

Least Common Multiple of 84,870,144 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 84,870,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(84,870,144) = 6

common factors(in case of two or more numbers have common factors) = 12

GCF(84,870,144) x common factors =6 x 12 = 72

LCM(84,870,144) = ( 84 × 870 × 144 ) / 72

LCM(84,870,144) = 10523520 / 72

LCM(84,870,144) = 146160

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FAQs on GCF of Fractions of 71/84, 89/870, 101/144

1. What is the HCF of 71,89,101?

The HCF of 71,89,101 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 71/84, 89/870, 101/144?

Answer: GCF of Numerators as per given numbers 71/84, 89/870, 101/144 is

GCF of Numerators i.e. for 71,89,101 is 1

LCM of denominators i.e. for 84,870,144 is 146160.

Thus, GCF of Fractions is 1/146160.Finally, GCF of Fractions for 71/84, 89/870, 101/144 is 1/146160.