How to Find GCF of 456/31, 770/974?

GCF of 456/31, 770/974

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 456/31, 770/974 i.e 2/30194 easily. The following is the detailed procedure to determine the greatest common factor of fractions 456/31, 770/974.

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 456/31,770/974?

Given fractions are 456/31,770/974

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 456/31,770/974, numerators are 456,770

Denominators are 31,974

The GCF of 456,770 is 2 .

LCM of 31,974 is 30194.

The greatest common factor of 456/31,770/974 = [GCF of 456,770]/[LCM of 31,974]= 2/30194

Therefore, the GCF of 456/31,770/974 is 2/30194.

Greatest Common Factor of 456,770

To find the highest common factor of 456,770, we have to find the factors of both numbers and list the highest common factor.

The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456

The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770

The HCF of 456,770 is 2.

Lets's calculate GCF of 456,770

Greatest Common Factor (GCF) of 456,770 By Common Division

2	456, 770
	228, 385

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

Greatest Common Factor of 456,770 By Matching Biggest Common Factor Method

Now, list down the factors of 456

1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456

Now, list down the factors of 770

1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770

Greatest Common Factor

We found the factors 456,770 . The biggest common factor number is the GCF number.
So the greatest common factor 456,770 is 2.

Lets's calculate LCM of 31,974

Lowest Common Multiple of 31,974 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 30194

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/30194

Therefore, the GCF of Fractions 456/31,770/974 is 2/30194

Least Common Multiple of 31,974 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 31,974 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,974) = 1

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

GCF(31,974) x common factors =1 x 1 = 1

LCM(31,974) = ( 31 × 974 ) / 1

LCM(31,974) = 30194 / 1

LCM(31,974) = 30194

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FAQs on GCF of Fractions of 456/31, 770/974

1. What is the HCF of 456,770?

The HCF of 456,770 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 456/31, 770/974?

Answer: GCF of Numerators as per given numbers 456/31, 770/974 is

GCF of Numerators i.e. for 456,770 is 2

LCM of denominators i.e. for 31,974 is 30194.

Thus, GCF of Fractions is 2/30194.Finally, GCF of Fractions for 456/31, 770/974 is 2/30194.