GCF of 490/14, 432/52, 400/52
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 490/14, 432/52, 400/52 i.e 2/364 easily. The following is the detailed procedure to determine the greatest common factor of fractions 490/14, 432/52, 400/52.
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 490/14,432/52,400/52?
Given fractions are 490/14,432/52,400/52
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 490/14,432/52,400/52, numerators are 490,432,400
Denominators are 14,52,52
The GCF of 490,432,400 is 2 .
LCM of 14,52,52 is 364.
The greatest common factor of 490/14,432/52,400/52 = [GCF of 490,432,400]/[LCM of 14,52,52]= 2/364
Therefore, the GCF of 490/14,432/52,400/52 is 2/364.
To find the highest common factor of 490,432,400, we have to find the factors of both numbers and list the highest common factor.
The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 490,432,400 is 2.
Lets's calculate GCF of 490,432,400
| 2 | 490, 432, 400 |
| 245, 216, 200 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 490,432,400 By Matching Biggest Common Factor Method
Now, list down the factors of 490
:1,2,5,7,10,14,35,49,70,98,245,490
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
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 490,432,400 . The biggest common factor number is the GCF number.
So the greatest common factor 490,432,400 is 2.
Lets's calculate LCM of 14,52,52
| 2 | 14, 52, 52 |
| 2 | 7, 26, 26 |
| 13 | 7, 13, 13 |
| 7, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 13 x 7 x 1 x 1 = 364
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/364
Therefore, the GCF of Fractions 490/14,432/52,400/52 is 2/364
Least Common Multiple of 14,52,52 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 14,52,52 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,52,52) = 2
common factors(in case of two or more numbers have common factors) = 52
GCF(14,52,52) x common factors =2 x 52 = 104
LCM(14,52,52) = ( 14 × 52 × 52 ) / 104
LCM(14,52,52) = 37856 / 104
LCM(14,52,52) = 364
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FAQs on GCF of Fractions of 490/14, 432/52, 400/52
1. What is the HCF of 490,432,400?
The HCF of 490,432,400 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 490/14, 432/52, 400/52?
Answer: GCF of Numerators as per given numbers 490/14, 432/52, 400/52 is
GCF of Numerators i.e. for 490,432,400 is 2
LCM of denominators i.e. for 14,52,52 is 364.
Thus, GCF of Fractions is 2/364.Finally, GCF of Fractions for 490/14, 432/52, 400/52 is 2/364.