How to Find GCF of 970/345, 3486/653?

GCF of 970/345, 3486/653

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 970/345, 3486/653 i.e 2/225285 easily. The following is the detailed procedure to determine the greatest common factor of fractions 970/345, 3486/653.

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 970/345,3486/653?

Given fractions are 970/345,3486/653

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 970/345,3486/653, numerators are 970,3486

Denominators are 345,653

The GCF of 970,3486 is 2 .

LCM of 345,653 is 225285.

The greatest common factor of 970/345,3486/653 = [GCF of 970,3486]/[LCM of 345,653]= 2/225285

Therefore, the GCF of 970/345,3486/653 is 2/225285.

Greatest Common Factor of 970,3486

To find the highest common factor of 970,3486, we have to find the factors of both numbers and list the highest common factor.

The factors of 970 are 1, 2, 5, 10, 97, 194, 485, 970

The factors of 3486 are 1, 2, 3, 6, 7, 14, 21, 42, 83, 166, 249, 498, 581, 1162, 1743, 3486

The HCF of 970,3486 is 2.

Lets's calculate GCF of 970,3486

Greatest Common Factor (GCF) of 970,3486 By Common Division

2	970, 3486
	485, 1743

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

Greatest Common Factor of 970,3486 By Matching Biggest Common Factor Method

Now, list down the factors of 970

1,2,5,10,97,194,485,970

Now, list down the factors of 3486

1,2,3,6,7,14,21,42,83,166,249,498,581,1162,1743,3486

Greatest Common Factor

We found the factors 970,3486 . The biggest common factor number is the GCF number.
So the greatest common factor 970,3486 is 2.

Lets's calculate LCM of 345,653

Lowest Common Multiple of 345,653 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 225285

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/225285

Therefore, the GCF of Fractions 970/345,3486/653 is 2/225285

Least Common Multiple of 345,653 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 345,653 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(345,653) = 1

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

GCF(345,653) x common factors =1 x 1 = 1

LCM(345,653) = ( 345 × 653 ) / 1

LCM(345,653) = 225285 / 1

LCM(345,653) = 225285

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FAQs on GCF of Fractions of 970/345, 3486/653

1. What is the HCF of 970,3486?

The HCF of 970,3486 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 970/345, 3486/653?

Answer: GCF of Numerators as per given numbers 970/345, 3486/653 is

GCF of Numerators i.e. for 970,3486 is 2

LCM of denominators i.e. for 345,653 is 225285.

Thus, GCF of Fractions is 2/225285.Finally, GCF of Fractions for 970/345, 3486/653 is 2/225285.