How to Find GCF of 1701/472, 9971/432?

GCF of 1701/472, 9971/432

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 1701/472, 9971/432 i.e 1/25488 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1701/472, 9971/432.

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 1701/472,9971/432?

Given fractions are 1701/472,9971/432

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 1701/472,9971/432, numerators are 1701,9971

Denominators are 472,432

The GCF of 1701,9971 is 1 .

LCM of 472,432 is 25488.

The greatest common factor of 1701/472,9971/432 = [GCF of 1701,9971]/[LCM of 472,432]= 1/25488

Therefore, the GCF of 1701/472,9971/432 is 1/25488.

Greatest Common Factor of 1701,9971

To find the highest common factor of 1701,9971, we have to find the factors of both numbers and list the highest common factor.

The factors of 1701 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 243, 567, 1701

The factors of 9971 are 1, 13, 59, 169, 767, 9971

The HCF of 1701,9971 is 1.

Lets's calculate GCF of 1701,9971

Greatest Common Factor (GCF) of 1701,9971 By Common Division

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

Greatest Common Factor of 1701,9971 By Matching Biggest Common Factor Method

Now, list down the factors of 1701

1,3,7,9,21,27,63,81,189,243,567,1701

Now, list down the factors of 9971

1,13,59,169,767,9971

Greatest Common Factor

We found the factors 1701,9971 . The biggest common factor number is the GCF number.
So the greatest common factor 1701,9971 is 1.

Lets's calculate LCM of 472,432

Lowest Common Multiple of 472,432 using Common Division

2	472, 432
2	236, 216
2	118, 108
	59, 54

∴ So the LCM of the given numbers is 2 x 2 x 2 x 59 x 54 = 25488

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25488

Therefore, the GCF of Fractions 1701/472,9971/432 is 1/25488

Least Common Multiple of 472,432 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 472,432 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(472,432) = 8

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

GCF(472,432) x common factors =8 x 1 = 8

LCM(472,432) = ( 472 × 432 ) / 8

LCM(472,432) = 203904 / 8

LCM(472,432) = 25488

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FAQs on GCF of Fractions of 1701/472, 9971/432

1. What is the HCF of 1701,9971?

The HCF of 1701,9971 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 1701/472, 9971/432?

Answer: GCF of Numerators as per given numbers 1701/472, 9971/432 is

GCF of Numerators i.e. for 1701,9971 is 1

LCM of denominators i.e. for 472,432 is 25488.

Thus, GCF of Fractions is 1/25488.Finally, GCF of Fractions for 1701/472, 9971/432 is 1/25488.