GCF of 562/66, 705/21, 212/50
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 562/66, 705/21, 212/50 i.e 1/11550 easily. The following is the detailed procedure to determine the greatest common factor of fractions 562/66, 705/21, 212/50.
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 562/66,705/21,212/50?
Given fractions are 562/66,705/21,212/50
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 562/66,705/21,212/50, numerators are 562,705,212
Denominators are 66,21,50
The GCF of 562,705,212 is 1 .
LCM of 66,21,50 is 11550.
The greatest common factor of 562/66,705/21,212/50 = [GCF of 562,705,212]/[LCM of 66,21,50]= 1/11550
Therefore, the GCF of 562/66,705/21,212/50 is 1/11550.
To find the highest common factor of 562,705,212, we have to find the factors of both numbers and list the highest common factor.
The factors of 562 are 1, 2, 281, 562
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The factors of 212 are 1, 2, 4, 53, 106, 212
The HCF of 562,705,212 is 1.
Lets's calculate GCF of 562,705,212
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 562,705,212 By Matching Biggest Common Factor Method
Now, list down the factors of 562
:1,2,281,562
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Now, list down the factors of 212
:1,2,4,53,106,212
Greatest Common Factor
We found the factors 562,705,212 . The biggest common factor number is the GCF number.
So the greatest common factor 562,705,212 is 1.
Lets's calculate LCM of 66,21,50
| 2 | 66, 21, 50 |
| 3 | 33, 21, 25 |
| 11, 7, 25 |
∴ So the LCM of the given numbers is 2 x 3 x 11 x 7 x 25 = 11550
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11550
Therefore, the GCF of Fractions 562/66,705/21,212/50 is 1/11550
Least Common Multiple of 66,21,50 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 66,21,50 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,21,50) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(66,21,50) x common factors =1 x 6 = 6
LCM(66,21,50) = ( 66 × 21 × 50 ) / 6
LCM(66,21,50) = 69300 / 6
LCM(66,21,50) = 11550
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FAQs on GCF of Fractions of 562/66, 705/21, 212/50
1. What is the HCF of 562,705,212?
The HCF of 562,705,212 is 1
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 562/66, 705/21, 212/50?
Answer: GCF of Numerators as per given numbers 562/66, 705/21, 212/50 is
GCF of Numerators i.e. for 562,705,212 is 1
LCM of denominators i.e. for 66,21,50 is 11550.
Thus, GCF of Fractions is 1/11550.Finally, GCF of Fractions for 562/66, 705/21, 212/50 is 1/11550.