How to Find GCF of 700/364, 9574/1216?

GCF of 700/364, 9574/1216

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 700/364, 9574/1216 i.e 2/110656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 700/364, 9574/1216.

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 700/364,9574/1216?

Given fractions are 700/364,9574/1216

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 700/364,9574/1216, numerators are 700,9574

Denominators are 364,1216

The GCF of 700,9574 is 2 .

LCM of 364,1216 is 110656.

The greatest common factor of 700/364,9574/1216 = [GCF of 700,9574]/[LCM of 364,1216]= 2/110656

Therefore, the GCF of 700/364,9574/1216 is 2/110656.

Greatest Common Factor of 700,9574

To find the highest common factor of 700,9574, we have to find the factors of both numbers and list the highest common factor.

The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700

The factors of 9574 are 1, 2, 4787, 9574

The HCF of 700,9574 is 2.

Lets's calculate GCF of 700,9574

Greatest Common Factor (GCF) of 700,9574 By Common Division

2	700, 9574
	350, 4787

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

Greatest Common Factor of 700,9574 By Matching Biggest Common Factor Method

Now, list down the factors of 700

1,2,4,5,7,10,14,20,25,28,35,50,70,100,140,175,350,700

Now, list down the factors of 9574

1,2,4787,9574

Greatest Common Factor

We found the factors 700,9574 . The biggest common factor number is the GCF number.
So the greatest common factor 700,9574 is 2.

Lets's calculate LCM of 364,1216

Lowest Common Multiple of 364,1216 using Common Division

2	364, 1216
2	182, 608
	91, 304

∴ So the LCM of the given numbers is 2 x 2 x 91 x 304 = 110656

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/110656

Therefore, the GCF of Fractions 700/364,9574/1216 is 2/110656

Least Common Multiple of 364,1216 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 364,1216 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(364,1216) = 4

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

GCF(364,1216) x common factors =4 x 1 = 4

LCM(364,1216) = ( 364 × 1216 ) / 4

LCM(364,1216) = 442624 / 4

LCM(364,1216) = 110656

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FAQs on GCF of Fractions of 700/364, 9574/1216

1. What is the HCF of 700,9574?

The HCF of 700,9574 is 2

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 700/364, 9574/1216?

Answer: GCF of Numerators as per given numbers 700/364, 9574/1216 is

GCF of Numerators i.e. for 700,9574 is 2

LCM of denominators i.e. for 364,1216 is 110656.

Thus, GCF of Fractions is 2/110656.Finally, GCF of Fractions for 700/364, 9574/1216 is 2/110656.