How to Find GCF of 700/33, 870/949?

GCF of 700/33, 870/949

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 700/33, 870/949 i.e 10/31317 easily. The following is the detailed procedure to determine the greatest common factor of fractions 700/33, 870/949.

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 700/33,870/949?

Given fractions are 700/33,870/949

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 700/33,870/949, numerators are 700,870

Denominators are 33,949

The GCF of 700,870 is 10 .

LCM of 33,949 is 31317.

The greatest common factor of 700/33,870/949 = [GCF of 700,870]/[LCM of 33,949]= 10/31317

Therefore, the GCF of 700/33,870/949 is 10/31317.

Greatest Common Factor of 700,870

To find the highest common factor of 700,870, 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 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

The HCF of 700,870 is 10.

Lets's calculate GCF of 700,870

Greatest Common Factor (GCF) of 700,870 By Common Division

2	700, 870
5	350, 435
	70, 87

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 700,870 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 870

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Greatest Common Factor

We found the factors 700,870 . The biggest common factor number is the GCF number.
So the greatest common factor 700,870 is 10.

Lets's calculate LCM of 33,949

Lowest Common Multiple of 33,949 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 31317

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/31317

Therefore, the GCF of Fractions 700/33,870/949 is 10/31317

Least Common Multiple of 33,949 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 33,949 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(33,949) = 1

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

GCF(33,949) x common factors =1 x 1 = 1

LCM(33,949) = ( 33 × 949 ) / 1

LCM(33,949) = 31317 / 1

LCM(33,949) = 31317

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 700/33, 870/949

1. What is the HCF of 700,870?

The HCF of 700,870 is 10

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 700/33, 870/949?

Answer: GCF of Numerators as per given numbers 700/33, 870/949 is

GCF of Numerators i.e. for 700,870 is 10

LCM of denominators i.e. for 33,949 is 31317.

Thus, GCF of Fractions is 10/31317.Finally, GCF of Fractions for 700/33, 870/949 is 10/31317.