GCF of 714/21, 312/42, 400/89
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 714/21, 312/42, 400/89 i.e 2/3738 easily. The following is the detailed procedure to determine the greatest common factor of fractions 714/21, 312/42, 400/89.
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 714/21,312/42,400/89?
Given fractions are 714/21,312/42,400/89
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 714/21,312/42,400/89, numerators are 714,312,400
Denominators are 21,42,89
The GCF of 714,312,400 is 2 .
LCM of 21,42,89 is 3738.
The greatest common factor of 714/21,312/42,400/89 = [GCF of 714,312,400]/[LCM of 21,42,89]= 2/3738
Therefore, the GCF of 714/21,312/42,400/89 is 2/3738.
To find the highest common factor of 714,312,400, we have to find the factors of both numbers and list the highest common factor.
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 714,312,400 is 2.
Lets's calculate GCF of 714,312,400
| 2 | 714, 312, 400 |
| 357, 156, 200 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 714,312,400 By Matching Biggest Common Factor Method
Now, list down the factors of 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 714,312,400 . The biggest common factor number is the GCF number.
So the greatest common factor 714,312,400 is 2.
Lets's calculate LCM of 21,42,89
| 3 | 21, 42, 89 |
| 7 | 7, 14, 89 |
| 1, 2, 89 |
∴ So the LCM of the given numbers is 3 x 7 x 1 x 2 x 89 = 3738
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3738
Therefore, the GCF of Fractions 714/21,312/42,400/89 is 2/3738
Least Common Multiple of 21,42,89 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 21,42,89 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,42,89) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(21,42,89) x common factors =1 x 21 = 21
LCM(21,42,89) = ( 21 × 42 × 89 ) / 21
LCM(21,42,89) = 78498 / 21
LCM(21,42,89) = 3738
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 714/21, 312/42, 400/89
1. What is the HCF of 714,312,400?
The HCF of 714,312,400 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 714/21, 312/42, 400/89?
Answer: GCF of Numerators as per given numbers 714/21, 312/42, 400/89 is
GCF of Numerators i.e. for 714,312,400 is 2
LCM of denominators i.e. for 21,42,89 is 3738.
Thus, GCF of Fractions is 2/3738.Finally, GCF of Fractions for 714/21, 312/42, 400/89 is 2/3738.