GCF of 3144/638, 3312/762
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3144/638, 3312/762 i.e 24/243078 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3144/638, 3312/762.
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 3144/638,3312/762?
Given fractions are 3144/638,3312/762
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 3144/638,3312/762, numerators are 3144,3312
Denominators are 638,762
The GCF of 3144,3312 is 24 .
LCM of 638,762 is 243078.
The greatest common factor of 3144/638,3312/762 = [GCF of 3144,3312]/[LCM of 638,762]= 24/243078
Therefore, the GCF of 3144/638,3312/762 is 24/243078.
To find the highest common factor of 3144,3312, we have to find the factors of both numbers and list the highest common factor.
The factors of 3144 are 1, 2, 3, 4, 6, 8, 12, 24, 131, 262, 393, 524, 786, 1048, 1572, 3144
The factors of 3312 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 23, 24, 36, 46, 48, 69, 72, 92, 138, 144, 184, 207, 276, 368, 414, 552, 828, 1104, 1656, 3312
The HCF of 3144,3312 is 24.
Lets's calculate GCF of 3144,3312
| 2 | 3144, 3312 |
| 2 | 1572, 1656 |
| 2 | 786, 828 |
| 3 | 393, 414 |
| 131, 138 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 3144,3312 By Matching Biggest Common Factor Method
Now, list down the factors of 3144
:1,2,3,4,6,8,12,24,131,262,393,524,786,1048,1572,3144
Now, list down the factors of 3312
:1,2,3,4,6,8,9,12,16,18,23,24,36,46,48,69,72,92,138,144,184,207,276,368,414,552,828,1104,1656,3312
Greatest Common Factor
We found the factors 3144,3312 . The biggest common factor number is the GCF number.
So the greatest common factor 3144,3312 is 24.
Lets's calculate LCM of 638,762
| 2 | 638, 762 |
| 319, 381 |
∴ So the LCM of the given numbers is 2 x 319 x 381 = 243078
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/243078
Therefore, the GCF of Fractions 3144/638,3312/762 is 24/243078
Least Common Multiple of 638,762 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 638,762 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(638,762) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(638,762) x common factors =2 x 1 = 2
LCM(638,762) = ( 638 × 762 ) / 2
LCM(638,762) = 486156 / 2
LCM(638,762) = 243078
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FAQs on GCF of Fractions of 3144/638, 3312/762
1. What is the HCF of 3144,3312?
The HCF of 3144,3312 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 3144/638, 3312/762?
Answer: GCF of Numerators as per given numbers 3144/638, 3312/762 is
GCF of Numerators i.e. for 3144,3312 is 24
LCM of denominators i.e. for 638,762 is 243078.
Thus, GCF of Fractions is 24/243078.Finally, GCF of Fractions for 3144/638, 3312/762 is 24/243078.