GCF of 441/132, 420/222
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 441/132, 420/222 i.e 21/4884 easily. The following is the detailed procedure to determine the greatest common factor of fractions 441/132, 420/222.
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 441/132,420/222?
Given fractions are 441/132,420/222
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 441/132,420/222, numerators are 441,420
Denominators are 132,222
The GCF of 441,420 is 21 .
LCM of 132,222 is 4884.
The greatest common factor of 441/132,420/222 = [GCF of 441,420]/[LCM of 132,222]= 21/4884
Therefore, the GCF of 441/132,420/222 is 21/4884.
To find the highest common factor of 441,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, 441
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 441,420 is 21.
Lets's calculate GCF of 441,420
| 3 | 441, 420 |
| 7 | 147, 140 |
| 21, 20 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 441,420 By Matching Biggest Common Factor Method
Now, list down the factors of 441
:1,3,7,9,21,49,63,147,441
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 441,420 . The biggest common factor number is the GCF number.
So the greatest common factor 441,420 is 21.
Lets's calculate LCM of 132,222
| 2 | 132, 222 |
| 3 | 66, 111 |
| 22, 37 |
∴ So the LCM of the given numbers is 2 x 3 x 22 x 37 = 4884
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/4884
Therefore, the GCF of Fractions 441/132,420/222 is 21/4884
Least Common Multiple of 132,222 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 132,222 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(132,222) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(132,222) x common factors =6 x 1 = 6
LCM(132,222) = ( 132 × 222 ) / 6
LCM(132,222) = 29304 / 6
LCM(132,222) = 4884
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FAQs on GCF of Fractions of 441/132, 420/222
1. What is the HCF of 441,420?
The HCF of 441,420 is 21
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 441/132, 420/222?
Answer: GCF of Numerators as per given numbers 441/132, 420/222 is
GCF of Numerators i.e. for 441,420 is 21
LCM of denominators i.e. for 132,222 is 4884.
Thus, GCF of Fractions is 21/4884.Finally, GCF of Fractions for 441/132, 420/222 is 21/4884.