How to Find GCF of 14/88, 49/67, 31/75, 22/205?

GCF of 14/88, 49/67, 31/75, 22/205

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 14/88, 49/67, 31/75, 22/205 i.e 1/18130200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/88, 49/67, 31/75, 22/205.

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 14/88,49/67,31/75,22/205?

Given fractions are 14/88,49/67,31/75,22/205

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 14/88,49/67,31/75,22/205, numerators are 14,49,31,22

Denominators are 88,67,75,205

The GCF of 14,49,31,22 is 1 .

LCM of 88,67,75,205 is 18130200.

The greatest common factor of 14/88,49/67,31/75,22/205 = [GCF of 14,49,31,22]/[LCM of 88,67,75,205]= 1/18130200

Therefore, the GCF of 14/88,49/67,31/75,22/205 is 1/18130200.

Greatest Common Factor of 14,49,31,22

To find the highest common factor of 14,49,31,22, we have to find the factors of both numbers and list the highest common factor.

The factors of 14 are 1, 2, 7, 14

The factors of 49 are 1, 7, 49

The factors of 31 are 1, 31

The factors of 22 are 1, 2, 11, 22

The HCF of 14,49,31,22 is 1.

Lets's calculate GCF of 14,49,31,22

Greatest Common Factor (GCF) of 14,49,31,22 By Common Division

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

Greatest Common Factor of 14,49,31,22 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 49

1,7,49

Now, list down the factors of 31

1,31

Now, list down the factors of 22

1,2,11,22

Greatest Common Factor

We found the factors 14,49,31,22 . The biggest common factor number is the GCF number.
So the greatest common factor 14,49,31,22 is 1.

Lets's calculate LCM of 88,67,75,205

Lowest Common Multiple of 88,67,75,205 using Common Division

5	88, 67, 75, 205
	88, 67, 15, 41

∴ So the LCM of the given numbers is 5 x 88 x 67 x 15 x 41 = 18130200

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18130200

Therefore, the GCF of Fractions 14/88,49/67,31/75,22/205 is 1/18130200

Least Common Multiple of 88,67,75,205 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 88,67,75,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(88,67,75,205) = 1

common factors(in case of two or more numbers have common factors) = 5

GCF(88,67,75,205) x common factors =1 x 5 = 5

LCM(88,67,75,205) = ( 88 × 67 × 75 × 205 ) / 5

LCM(88,67,75,205) = 90651000 / 5

LCM(88,67,75,205) = 18130200

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 14/88, 49/67, 31/75, 22/205

1. What is the HCF of 14,49,31,22?

The HCF of 14,49,31,22 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 14/88, 49/67, 31/75, 22/205?

Answer: GCF of Numerators as per given numbers 14/88, 49/67, 31/75, 22/205 is

GCF of Numerators i.e. for 14,49,31,22 is 1

LCM of denominators i.e. for 88,67,75,205 is 18130200.

Thus, GCF of Fractions is 1/18130200.Finally, GCF of Fractions for 14/88, 49/67, 31/75, 22/205 is 1/18130200.