How to Find GCF of 67/32, 410/92, 421/116?

GCF of 67/32, 410/92, 421/116

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 67/32, 410/92, 421/116 i.e 1/21344 easily. The following is the detailed procedure to determine the greatest common factor of fractions 67/32, 410/92, 421/116.

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 67/32,410/92,421/116?

Given fractions are 67/32,410/92,421/116

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 67/32,410/92,421/116, numerators are 67,410,421

Denominators are 32,92,116

The GCF of 67,410,421 is 1 .

LCM of 32,92,116 is 21344.

The greatest common factor of 67/32,410/92,421/116 = [GCF of 67,410,421]/[LCM of 32,92,116]= 1/21344

Therefore, the GCF of 67/32,410/92,421/116 is 1/21344.

Greatest Common Factor of 67,410,421

To find the highest common factor of 67,410,421, we have to find the factors of both numbers and list the highest common factor.

The factors of 67 are 1, 67

The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410

The factors of 421 are 1, 421

The HCF of 67,410,421 is 1.

Lets's calculate GCF of 67,410,421

Greatest Common Factor (GCF) of 67,410,421 By Common Division

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

Greatest Common Factor of 67,410,421 By Matching Biggest Common Factor Method

Now, list down the factors of 67

1,67

Now, list down the factors of 410

1,2,5,10,41,82,205,410

Now, list down the factors of 421

1,421

Greatest Common Factor

We found the factors 67,410,421 . The biggest common factor number is the GCF number.
So the greatest common factor 67,410,421 is 1.

Lets's calculate LCM of 32,92,116

Lowest Common Multiple of 32,92,116 using Common Division

2	32, 92, 116
2	16, 46, 58
	8, 23, 29

∴ So the LCM of the given numbers is 2 x 2 x 8 x 23 x 29 = 21344

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21344

Therefore, the GCF of Fractions 67/32,410/92,421/116 is 1/21344

Least Common Multiple of 32,92,116 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 32,92,116 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(32,92,116) = 4

common factors(in case of two or more numbers have common factors) = 4

GCF(32,92,116) x common factors =4 x 4 = 16

LCM(32,92,116) = ( 32 × 92 × 116 ) / 16

LCM(32,92,116) = 341504 / 16

LCM(32,92,116) = 21344

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FAQs on GCF of Fractions of 67/32, 410/92, 421/116

1. What is the HCF of 67,410,421?

The HCF of 67,410,421 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 67/32, 410/92, 421/116?

Answer: GCF of Numerators as per given numbers 67/32, 410/92, 421/116 is

GCF of Numerators i.e. for 67,410,421 is 1

LCM of denominators i.e. for 32,92,116 is 21344.

Thus, GCF of Fractions is 1/21344.Finally, GCF of Fractions for 67/32, 410/92, 421/116 is 1/21344.