How to Find GCF of 37/205, 92/187, 214/824?

GCF of 37/205, 92/187, 214/824

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 37/205, 92/187, 214/824 i.e 1/31588040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 37/205, 92/187, 214/824.

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 37/205,92/187,214/824?

Given fractions are 37/205,92/187,214/824

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 37/205,92/187,214/824, numerators are 37,92,214

Denominators are 205,187,824

The GCF of 37,92,214 is 1 .

LCM of 205,187,824 is 31588040.

The greatest common factor of 37/205,92/187,214/824 = [GCF of 37,92,214]/[LCM of 205,187,824]= 1/31588040

Therefore, the GCF of 37/205,92/187,214/824 is 1/31588040.

Greatest Common Factor of 37,92,214

To find the highest common factor of 37,92,214, we have to find the factors of both numbers and list the highest common factor.

The factors of 37 are 1, 37

The factors of 92 are 1, 2, 4, 23, 46, 92

The factors of 214 are 1, 2, 107, 214

The HCF of 37,92,214 is 1.

Lets's calculate GCF of 37,92,214

Greatest Common Factor (GCF) of 37,92,214 By Common Division

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

Greatest Common Factor of 37,92,214 By Matching Biggest Common Factor Method

Now, list down the factors of 37

1,37

Now, list down the factors of 92

1,2,4,23,46,92

Now, list down the factors of 214

1,2,107,214

Greatest Common Factor

We found the factors 37,92,214 . The biggest common factor number is the GCF number.
So the greatest common factor 37,92,214 is 1.

Lets's calculate LCM of 205,187,824

Lowest Common Multiple of 205,187,824 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 31588040

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31588040

Therefore, the GCF of Fractions 37/205,92/187,214/824 is 1/31588040

Least Common Multiple of 205,187,824 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 205,187,824 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(205,187,824) = 1

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

GCF(205,187,824) x common factors =1 x 1 = 1

LCM(205,187,824) = ( 205 × 187 × 824 ) / 1

LCM(205,187,824) = 31588040 / 1

LCM(205,187,824) = 31588040

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FAQs on GCF of Fractions of 37/205, 92/187, 214/824

1. What is the HCF of 37,92,214?

The HCF of 37,92,214 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 37/205, 92/187, 214/824?

Answer: GCF of Numerators as per given numbers 37/205, 92/187, 214/824 is

GCF of Numerators i.e. for 37,92,214 is 1

LCM of denominators i.e. for 205,187,824 is 31588040.

Thus, GCF of Fractions is 1/31588040.Finally, GCF of Fractions for 37/205, 92/187, 214/824 is 1/31588040.