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GCF of 284/23, 208/143

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 284/23, 208/143 i.e 4/3289 easily. The following is the detailed procedure to determine the greatest common factor of fractions 284/23, 208/143.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 284/23,208/143?

Given fractions are 284/23,208/143

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 284/23,208/143, numerators are 284,208

Denominators are 23,143

The GCF of 284,208 is 4 .

LCM of 23,143 is 3289.

The greatest common factor of 284/23,208/143 = [GCF of 284,208]/[LCM of 23,143]= 4/3289

Therefore, the GCF of 284/23,208/143 is 4/3289.

Greatest Common Factor of 284,208

To find the highest common factor of 284,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 284 are 1, 2, 4, 71, 142, 284

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 284,208 is 4.

Lets's calculate GCF of 284,208

Greatest Common Factor (GCF) of 284,208 By Common Division

2 284, 208
2 142, 104
71, 52

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 284,208 By Matching Biggest Common Factor Method

Greatest Common Factor of 284,208 By Matching Biggest Common Factor Method

Now, list down the factors of 284

:

1,2,4,71,142,284

Now, list down the factors of 208

:

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 284,208 . The biggest common factor number is the GCF number.
So the greatest common factor 284,208 is 4.

Lets's calculate LCM of 23,143

Lowest Common Multiple of 23,143 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3289

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/3289

Therefore, the GCF of Fractions 284/23,208/143 is 4/3289

Least Common Multiple of 23,143 with GCF Formula

Least Common Multiple of 23,143 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 23,143 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,143) = 1

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

GCF(23,143) x common factors =1 x 1 = 1

LCM(23,143) = ( 23 × 143 ) / 1

LCM(23,143) = 3289 / 1

LCM(23,143) = 3289


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FAQs on GCF of Fractions of 284/23, 208/143

1. What is the HCF of 284,208?

The HCF of 284,208 is 4

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 284/23, 208/143?

Answer: GCF of Numerators as per given numbers 284/23, 208/143 is

GCF of Numerators i.e. for 284,208 is 4

LCM of denominators i.e. for 23,143 is 3289.

Thus, GCF of Fractions is 4/3289.Finally, GCF of Fractions for 284/23, 208/143 is 4/3289.