How to Find GCF of 169/700, 7657/213?

GCF of 169/700, 7657/213

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 169/700, 7657/213 i.e 13/149100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 169/700, 7657/213.

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 169/700,7657/213?

Given fractions are 169/700,7657/213

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 169/700,7657/213, numerators are 169,7657

Denominators are 700,213

The GCF of 169,7657 is 13 .

LCM of 700,213 is 149100.

The greatest common factor of 169/700,7657/213 = [GCF of 169,7657]/[LCM of 700,213]= 13/149100

Therefore, the GCF of 169/700,7657/213 is 13/149100.

Greatest Common Factor of 169,7657

To find the highest common factor of 169,7657, we have to find the factors of both numbers and list the highest common factor.

The factors of 169 are 1, 13, 169

The factors of 7657 are 1, 13, 19, 31, 247, 403, 589, 7657

The HCF of 169,7657 is 13.

Lets's calculate GCF of 169,7657

Greatest Common Factor (GCF) of 169,7657 By Common Division

13	169, 7657
	13, 589

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 169,7657 By Matching Biggest Common Factor Method

Now, list down the factors of 169

1,13,169

Now, list down the factors of 7657

1,13,19,31,247,403,589,7657

Greatest Common Factor

We found the factors 169,7657 . The biggest common factor number is the GCF number.
So the greatest common factor 169,7657 is 13.

Lets's calculate LCM of 700,213

Lowest Common Multiple of 700,213 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 149100

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/149100

Therefore, the GCF of Fractions 169/700,7657/213 is 13/149100

Least Common Multiple of 700,213 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 700,213 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(700,213) = 1

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

GCF(700,213) x common factors =1 x 1 = 1

LCM(700,213) = ( 700 × 213 ) / 1

LCM(700,213) = 149100 / 1

LCM(700,213) = 149100

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FAQs on GCF of Fractions of 169/700, 7657/213

1. What is the HCF of 169,7657?

The HCF of 169,7657 is 13

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 169/700, 7657/213?

Answer: GCF of Numerators as per given numbers 169/700, 7657/213 is

GCF of Numerators i.e. for 169,7657 is 13

LCM of denominators i.e. for 700,213 is 149100.

Thus, GCF of Fractions is 13/149100.Finally, GCF of Fractions for 169/700, 7657/213 is 13/149100.