How to Find GCF of 39/219, 31/315, 907/749?

GCF of 39/219, 31/315, 907/749

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 39/219, 31/315, 907/749 i.e 1/2460465 easily. The following is the detailed procedure to determine the greatest common factor of fractions 39/219, 31/315, 907/749.

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 39/219,31/315,907/749?

Given fractions are 39/219,31/315,907/749

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 39/219,31/315,907/749, numerators are 39,31,907

Denominators are 219,315,749

The GCF of 39,31,907 is 1 .

LCM of 219,315,749 is 2460465.

The greatest common factor of 39/219,31/315,907/749 = [GCF of 39,31,907]/[LCM of 219,315,749]= 1/2460465

Therefore, the GCF of 39/219,31/315,907/749 is 1/2460465.

Greatest Common Factor of 39,31,907

To find the highest common factor of 39,31,907, we have to find the factors of both numbers and list the highest common factor.

The factors of 39 are 1, 3, 13, 39

The factors of 31 are 1, 31

The factors of 907 are 1, 907

The HCF of 39,31,907 is 1.

Lets's calculate GCF of 39,31,907

Greatest Common Factor (GCF) of 39,31,907 By Common Division

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

Greatest Common Factor of 39,31,907 By Matching Biggest Common Factor Method

Now, list down the factors of 39

1,3,13,39

Now, list down the factors of 31

1,31

Now, list down the factors of 907

1,907

Greatest Common Factor

We found the factors 39,31,907 . The biggest common factor number is the GCF number.
So the greatest common factor 39,31,907 is 1.

Lets's calculate LCM of 219,315,749

Lowest Common Multiple of 219,315,749 using Common Division

3	219, 315, 749
7	73, 105, 749
	73, 15, 107

∴ So the LCM of the given numbers is 3 x 7 x 73 x 15 x 107 = 2460465

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2460465

Therefore, the GCF of Fractions 39/219,31/315,907/749 is 1/2460465

Least Common Multiple of 219,315,749 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 219,315,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(219,315,749) = 1

common factors(in case of two or more numbers have common factors) = 21

GCF(219,315,749) x common factors =1 x 21 = 21

LCM(219,315,749) = ( 219 × 315 × 749 ) / 21

LCM(219,315,749) = 51669765 / 21

LCM(219,315,749) = 2460465

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FAQs on GCF of Fractions of 39/219, 31/315, 907/749

1. What is the HCF of 39,31,907?

The HCF of 39,31,907 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 39/219, 31/315, 907/749?

Answer: GCF of Numerators as per given numbers 39/219, 31/315, 907/749 is

GCF of Numerators i.e. for 39,31,907 is 1

LCM of denominators i.e. for 219,315,749 is 2460465.

Thus, GCF of Fractions is 1/2460465.Finally, GCF of Fractions for 39/219, 31/315, 907/749 is 1/2460465.