How to Find GCF of 30/68, 57/168, 971/412?

GCF of 30/68, 57/168, 971/412

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 30/68, 57/168, 971/412 i.e 1/294168 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/68, 57/168, 971/412.

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 30/68,57/168,971/412?

Given fractions are 30/68,57/168,971/412

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 30/68,57/168,971/412, numerators are 30,57,971

Denominators are 68,168,412

The GCF of 30,57,971 is 1 .

LCM of 68,168,412 is 294168.

The greatest common factor of 30/68,57/168,971/412 = [GCF of 30,57,971]/[LCM of 68,168,412]= 1/294168

Therefore, the GCF of 30/68,57/168,971/412 is 1/294168.

Greatest Common Factor of 30,57,971

To find the highest common factor of 30,57,971, we have to find the factors of both numbers and list the highest common factor.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 57 are 1, 3, 19, 57

The factors of 971 are 1, 971

The HCF of 30,57,971 is 1.

Lets's calculate GCF of 30,57,971

Greatest Common Factor (GCF) of 30,57,971 By Common Division

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

Greatest Common Factor of 30,57,971 By Matching Biggest Common Factor Method

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 57

1,3,19,57

Now, list down the factors of 971

1,971

Greatest Common Factor

We found the factors 30,57,971 . The biggest common factor number is the GCF number.
So the greatest common factor 30,57,971 is 1.

Lets's calculate LCM of 68,168,412

Lowest Common Multiple of 68,168,412 using Common Division

2	68, 168, 412
2	34, 84, 206
	17, 42, 103

∴ So the LCM of the given numbers is 2 x 2 x 17 x 42 x 103 = 294168

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/294168

Therefore, the GCF of Fractions 30/68,57/168,971/412 is 1/294168

Least Common Multiple of 68,168,412 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 68,168,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,168,412) = 4

common factors(in case of two or more numbers have common factors) = 4

GCF(68,168,412) x common factors =4 x 4 = 16

LCM(68,168,412) = ( 68 × 168 × 412 ) / 16

LCM(68,168,412) = 4706688 / 16

LCM(68,168,412) = 294168

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 30/68, 57/168, 971/412

1. What is the HCF of 30,57,971?

The HCF of 30,57,971 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 30/68, 57/168, 971/412?

Answer: GCF of Numerators as per given numbers 30/68, 57/168, 971/412 is

GCF of Numerators i.e. for 30,57,971 is 1

LCM of denominators i.e. for 68,168,412 is 294168.

Thus, GCF of Fractions is 1/294168.Finally, GCF of Fractions for 30/68, 57/168, 971/412 is 1/294168.