How to Find GCF of 31/65, 762/33, 313/693?

GCF of 31/65, 762/33, 313/693

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 31/65, 762/33, 313/693 i.e 1/45045 easily. The following is the detailed procedure to determine the greatest common factor of fractions 31/65, 762/33, 313/693.

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 31/65,762/33,313/693?

Given fractions are 31/65,762/33,313/693

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 31/65,762/33,313/693, numerators are 31,762,313

Denominators are 65,33,693

The GCF of 31,762,313 is 1 .

LCM of 65,33,693 is 45045.

The greatest common factor of 31/65,762/33,313/693 = [GCF of 31,762,313]/[LCM of 65,33,693]= 1/45045

Therefore, the GCF of 31/65,762/33,313/693 is 1/45045.

Greatest Common Factor of 31,762,313

To find the highest common factor of 31,762,313, we have to find the factors of both numbers and list the highest common factor.

The factors of 31 are 1, 31

The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762

The factors of 313 are 1, 313

The HCF of 31,762,313 is 1.

Lets's calculate GCF of 31,762,313

Greatest Common Factor (GCF) of 31,762,313 By Common Division

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

Greatest Common Factor of 31,762,313 By Matching Biggest Common Factor Method

Now, list down the factors of 31

1,31

Now, list down the factors of 762

1,2,3,6,127,254,381,762

Now, list down the factors of 313

1,313

Greatest Common Factor

We found the factors 31,762,313 . The biggest common factor number is the GCF number.
So the greatest common factor 31,762,313 is 1.

Lets's calculate LCM of 65,33,693

Lowest Common Multiple of 65,33,693 using Common Division

3	65, 33, 693
11	65, 11, 231
	65, 1, 21

∴ So the LCM of the given numbers is 3 x 11 x 65 x 1 x 21 = 45045

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/45045

Therefore, the GCF of Fractions 31/65,762/33,313/693 is 1/45045

Least Common Multiple of 65,33,693 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 65,33,693 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,33,693) = 1

common factors(in case of two or more numbers have common factors) = 33

GCF(65,33,693) x common factors =1 x 33 = 33

LCM(65,33,693) = ( 65 × 33 × 693 ) / 33

LCM(65,33,693) = 1486485 / 33

LCM(65,33,693) = 45045

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FAQs on GCF of Fractions of 31/65, 762/33, 313/693

1. What is the HCF of 31,762,313?

The HCF of 31,762,313 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 31/65, 762/33, 313/693?

Answer: GCF of Numerators as per given numbers 31/65, 762/33, 313/693 is

GCF of Numerators i.e. for 31,762,313 is 1

LCM of denominators i.e. for 65,33,693 is 45045.

Thus, GCF of Fractions is 1/45045.Finally, GCF of Fractions for 31/65, 762/33, 313/693 is 1/45045.