How to Find GCF of 73/213, 39/852, 682/412?

GCF of 73/213, 39/852, 682/412

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 73/213, 39/852, 682/412 i.e 1/87756 easily. The following is the detailed procedure to determine the greatest common factor of fractions 73/213, 39/852, 682/412.

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 73/213,39/852,682/412?

Given fractions are 73/213,39/852,682/412

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 73/213,39/852,682/412, numerators are 73,39,682

Denominators are 213,852,412

The GCF of 73,39,682 is 1 .

LCM of 213,852,412 is 87756.

The greatest common factor of 73/213,39/852,682/412 = [GCF of 73,39,682]/[LCM of 213,852,412]= 1/87756

Therefore, the GCF of 73/213,39/852,682/412 is 1/87756.

Greatest Common Factor of 73,39,682

To find the highest common factor of 73,39,682, we have to find the factors of both numbers and list the highest common factor.

The factors of 73 are 1, 73

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

The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682

The HCF of 73,39,682 is 1.

Lets's calculate GCF of 73,39,682

Greatest Common Factor (GCF) of 73,39,682 By Common Division

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

Greatest Common Factor of 73,39,682 By Matching Biggest Common Factor Method

Now, list down the factors of 73

1,73

Now, list down the factors of 39

1,3,13,39

Now, list down the factors of 682

1,2,11,22,31,62,341,682

Greatest Common Factor

We found the factors 73,39,682 . The biggest common factor number is the GCF number.
So the greatest common factor 73,39,682 is 1.

Lets's calculate LCM of 213,852,412

Lowest Common Multiple of 213,852,412 using Common Division

2	213, 852, 412
2	213, 426, 206
3	213, 213, 103
71	71, 71, 103
	1, 1, 103

∴ So the LCM of the given numbers is 2 x 2 x 3 x 71 x 1 x 1 x 103 = 87756

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/87756

Therefore, the GCF of Fractions 73/213,39/852,682/412 is 1/87756

Least Common Multiple of 213,852,412 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 213,852,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(213,852,412) = 1

common factors(in case of two or more numbers have common factors) = 852

GCF(213,852,412) x common factors =1 x 852 = 852

LCM(213,852,412) = ( 213 × 852 × 412 ) / 852

LCM(213,852,412) = 74768112 / 852

LCM(213,852,412) = 87756

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 73/213, 39/852, 682/412

1. What is the HCF of 73,39,682?

The HCF of 73,39,682 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 73/213, 39/852, 682/412?

Answer: GCF of Numerators as per given numbers 73/213, 39/852, 682/412 is

GCF of Numerators i.e. for 73,39,682 is 1

LCM of denominators i.e. for 213,852,412 is 87756.

Thus, GCF of Fractions is 1/87756.Finally, GCF of Fractions for 73/213, 39/852, 682/412 is 1/87756.