How to Find GCF of 700/22, 300/460?

GCF of 700/22, 300/460

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 700/22, 300/460 i.e 100/5060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 700/22, 300/460.

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 700/22,300/460?

Given fractions are 700/22,300/460

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 700/22,300/460, numerators are 700,300

Denominators are 22,460

The GCF of 700,300 is 100 .

LCM of 22,460 is 5060.

The greatest common factor of 700/22,300/460 = [GCF of 700,300]/[LCM of 22,460]= 100/5060

Therefore, the GCF of 700/22,300/460 is 100/5060.

Greatest Common Factor of 700,300

To find the highest common factor of 700,300, 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 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

The HCF of 700,300 is 100.

Lets's calculate GCF of 700,300

Greatest Common Factor (GCF) of 700,300 By Common Division

2	700, 300
2	350, 150
5	175, 75
5	35, 15
	7, 3

∴ So the GCF of the given numbers is 2 x 2 x 5 x 5 = 100

Greatest Common Factor of 700,300 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 300

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Greatest Common Factor

We found the factors 700,300 . The biggest common factor number is the GCF number.
So the greatest common factor 700,300 is 100.

Lets's calculate LCM of 22,460

Lowest Common Multiple of 22,460 using Common Division

2	22, 460
	11, 230

∴ So the LCM of the given numbers is 2 x 11 x 230 = 5060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 100/5060

Therefore, the GCF of Fractions 700/22,300/460 is 100/5060

Least Common Multiple of 22,460 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 22,460 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(22,460) = 2

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

GCF(22,460) x common factors =2 x 1 = 2

LCM(22,460) = ( 22 × 460 ) / 2

LCM(22,460) = 10120 / 2

LCM(22,460) = 5060

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 700/22, 300/460

1. What is the HCF of 700,300?

The HCF of 700,300 is 100

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 700/22, 300/460?

Answer: GCF of Numerators as per given numbers 700/22, 300/460 is

GCF of Numerators i.e. for 700,300 is 100

LCM of denominators i.e. for 22,460 is 5060.

Thus, GCF of Fractions is 100/5060.Finally, GCF of Fractions for 700/22, 300/460 is 100/5060.