How to Find GCF of 30/25, 70/57, 364/778?

GCF of 30/25, 70/57, 364/778

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 30/25, 70/57, 364/778 i.e 2/1108650 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/25, 70/57, 364/778.

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 30/25,70/57,364/778?

Given fractions are 30/25,70/57,364/778

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 30/25,70/57,364/778, numerators are 30,70,364

Denominators are 25,57,778

The GCF of 30,70,364 is 2 .

LCM of 25,57,778 is 1108650.

The greatest common factor of 30/25,70/57,364/778 = [GCF of 30,70,364]/[LCM of 25,57,778]= 2/1108650

Therefore, the GCF of 30/25,70/57,364/778 is 2/1108650.

Greatest Common Factor of 30,70,364

To find the highest common factor of 30,70,364, 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 70 are 1, 2, 5, 7, 10, 14, 35, 70

The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364

The HCF of 30,70,364 is 2.

Lets's calculate GCF of 30,70,364

Greatest Common Factor (GCF) of 30,70,364 By Common Division

2	30, 70, 364
	15, 35, 182

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 30,70,364 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 70

1,2,5,7,10,14,35,70

Now, list down the factors of 364

1,2,4,7,13,14,26,28,52,91,182,364

Greatest Common Factor

We found the factors 30,70,364 . The biggest common factor number is the GCF number.
So the greatest common factor 30,70,364 is 2.

Lets's calculate LCM of 25,57,778

Lowest Common Multiple of 25,57,778 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1108650

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1108650

Therefore, the GCF of Fractions 30/25,70/57,364/778 is 2/1108650

Least Common Multiple of 25,57,778 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 25,57,778 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(25,57,778) = 1

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

GCF(25,57,778) x common factors =1 x 1 = 1

LCM(25,57,778) = ( 25 × 57 × 778 ) / 1

LCM(25,57,778) = 1108650 / 1

LCM(25,57,778) = 1108650

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 30/25, 70/57, 364/778

1. What is the HCF of 30,70,364?

The HCF of 30,70,364 is 2

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 30/25, 70/57, 364/778?

Answer: GCF of Numerators as per given numbers 30/25, 70/57, 364/778 is

GCF of Numerators i.e. for 30,70,364 is 2

LCM of denominators i.e. for 25,57,778 is 1108650.

Thus, GCF of Fractions is 2/1108650.Finally, GCF of Fractions for 30/25, 70/57, 364/778 is 2/1108650.