GCF of 144/634, 312/450
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 144/634, 312/450 i.e 24/142650 easily. The following is the detailed procedure to determine the greatest common factor of fractions 144/634, 312/450.
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 144/634,312/450?
Given fractions are 144/634,312/450
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 144/634,312/450, numerators are 144,312
Denominators are 634,450
The GCF of 144,312 is 24 .
LCM of 634,450 is 142650.
The greatest common factor of 144/634,312/450 = [GCF of 144,312]/[LCM of 634,450]= 24/142650
Therefore, the GCF of 144/634,312/450 is 24/142650.
To find the highest common factor of 144,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 144,312 is 24.
Lets's calculate GCF of 144,312
| 2 | 144, 312 |
| 2 | 72, 156 |
| 2 | 36, 78 |
| 3 | 18, 39 |
| 6, 13 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 144,312 By Matching Biggest Common Factor Method
Now, list down the factors of 144
:1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 144,312 . The biggest common factor number is the GCF number.
So the greatest common factor 144,312 is 24.
Lets's calculate LCM of 634,450
| 2 | 634, 450 |
| 317, 225 |
∴ So the LCM of the given numbers is 2 x 317 x 225 = 142650
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/142650
Therefore, the GCF of Fractions 144/634,312/450 is 24/142650
Least Common Multiple of 634,450 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 634,450 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(634,450) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(634,450) x common factors =2 x 1 = 2
LCM(634,450) = ( 634 × 450 ) / 2
LCM(634,450) = 285300 / 2
LCM(634,450) = 142650
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FAQs on GCF of Fractions of 144/634, 312/450
1. What is the HCF of 144,312?
The HCF of 144,312 is 24
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 144/634, 312/450?
Answer: GCF of Numerators as per given numbers 144/634, 312/450 is
GCF of Numerators i.e. for 144,312 is 24
LCM of denominators i.e. for 634,450 is 142650.
Thus, GCF of Fractions is 24/142650.Finally, GCF of Fractions for 144/634, 312/450 is 24/142650.