How to Find GCF of 452/37, 414/2970?

GCF of 452/37, 414/2970

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 452/37, 414/2970 i.e 2/109890 easily. The following is the detailed procedure to determine the greatest common factor of fractions 452/37, 414/2970.

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 452/37,414/2970?

Given fractions are 452/37,414/2970

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 452/37,414/2970, numerators are 452,414

Denominators are 37,2970

The GCF of 452,414 is 2 .

LCM of 37,2970 is 109890.

The greatest common factor of 452/37,414/2970 = [GCF of 452,414]/[LCM of 37,2970]= 2/109890

Therefore, the GCF of 452/37,414/2970 is 2/109890.

Greatest Common Factor of 452,414

To find the highest common factor of 452,414, we have to find the factors of both numbers and list the highest common factor.

The factors of 452 are 1, 2, 4, 113, 226, 452

The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

The HCF of 452,414 is 2.

Lets's calculate GCF of 452,414

Greatest Common Factor (GCF) of 452,414 By Common Division

2	452, 414
	226, 207

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

Greatest Common Factor of 452,414 By Matching Biggest Common Factor Method

Now, list down the factors of 452

1,2,4,113,226,452

Now, list down the factors of 414

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 452,414 . The biggest common factor number is the GCF number.
So the greatest common factor 452,414 is 2.

Lets's calculate LCM of 37,2970

Lowest Common Multiple of 37,2970 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 109890

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/109890

Therefore, the GCF of Fractions 452/37,414/2970 is 2/109890

Least Common Multiple of 37,2970 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 37,2970 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(37,2970) = 1

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

GCF(37,2970) x common factors =1 x 1 = 1

LCM(37,2970) = ( 37 × 2970 ) / 1

LCM(37,2970) = 109890 / 1

LCM(37,2970) = 109890

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FAQs on GCF of Fractions of 452/37, 414/2970

1. What is the HCF of 452,414?

The HCF of 452,414 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 452/37, 414/2970?

Answer: GCF of Numerators as per given numbers 452/37, 414/2970 is

GCF of Numerators i.e. for 452,414 is 2

LCM of denominators i.e. for 37,2970 is 109890.

Thus, GCF of Fractions is 2/109890.Finally, GCF of Fractions for 452/37, 414/2970 is 2/109890.