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GCF of 464/68, 208/258

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 464/68, 208/258 i.e 16/8772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 464/68, 208/258.

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 464/68,208/258?

Given fractions are 464/68,208/258

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 464/68,208/258, numerators are 464,208

Denominators are 68,258

The GCF of 464,208 is 16 .

LCM of 68,258 is 8772.

The greatest common factor of 464/68,208/258 = [GCF of 464,208]/[LCM of 68,258]= 16/8772

Therefore, the GCF of 464/68,208/258 is 16/8772.

Greatest Common Factor of 464,208

To find the highest common factor of 464,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, 464

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

The HCF of 464,208 is 16.

Lets's calculate GCF of 464,208

Greatest Common Factor (GCF) of 464,208 By Common Division

2 464, 208
2 232, 104
2 116, 52
2 58, 26
29, 13

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 464,208 By Matching Biggest Common Factor Method

Greatest Common Factor of 464,208 By Matching Biggest Common Factor Method

Now, list down the factors of 464

:

1,2,4,8,16,29,58,116,232,464

Now, list down the factors of 208

:

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

Greatest Common Factor

We found the factors 464,208 . The biggest common factor number is the GCF number.
So the greatest common factor 464,208 is 16.

Lets's calculate LCM of 68,258

Lowest Common Multiple of 68,258 using Common Division

2 68, 258
34, 129

∴ So the LCM of the given numbers is 2 x 34 x 129 = 8772

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/8772

Therefore, the GCF of Fractions 464/68,208/258 is 16/8772

Least Common Multiple of 68,258 with GCF Formula

Least Common Multiple of 68,258 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 68,258 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,258) = 2

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

GCF(68,258) x common factors =2 x 1 = 2

LCM(68,258) = ( 68 × 258 ) / 2

LCM(68,258) = 17544 / 2

LCM(68,258) = 8772


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FAQs on GCF of Fractions of 464/68, 208/258

1. What is the HCF of 464,208?

The HCF of 464,208 is 16

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 464/68, 208/258?

Answer: GCF of Numerators as per given numbers 464/68, 208/258 is

GCF of Numerators i.e. for 464,208 is 16

LCM of denominators i.e. for 68,258 is 8772.

Thus, GCF of Fractions is 16/8772.Finally, GCF of Fractions for 464/68, 208/258 is 16/8772.