GCF of 64/348, 42/413, 456/315
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 64/348, 42/413, 456/315 i.e 2/2155860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 64/348, 42/413, 456/315.
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 64/348,42/413,456/315?
Given fractions are 64/348,42/413,456/315
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 64/348,42/413,456/315, numerators are 64,42,456
Denominators are 348,413,315
The GCF of 64,42,456 is 2 .
LCM of 348,413,315 is 2155860.
The greatest common factor of 64/348,42/413,456/315 = [GCF of 64,42,456]/[LCM of 348,413,315]= 2/2155860
Therefore, the GCF of 64/348,42/413,456/315 is 2/2155860.
To find the highest common factor of 64,42,456, we have to find the factors of both numbers and list the highest common factor.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 64,42,456 is 2.
Lets's calculate GCF of 64,42,456
| 2 | 64, 42, 456 |
| 32, 21, 228 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 64,42,456 By Matching Biggest Common Factor Method
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 64,42,456 . The biggest common factor number is the GCF number.
So the greatest common factor 64,42,456 is 2.
Lets's calculate LCM of 348,413,315
| 3 | 348, 413, 315 |
| 7 | 116, 413, 105 |
| 116, 59, 15 |
∴ So the LCM of the given numbers is 3 x 7 x 116 x 59 x 15 = 2155860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2155860
Therefore, the GCF of Fractions 64/348,42/413,456/315 is 2/2155860
Least Common Multiple of 348,413,315 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 348,413,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(348,413,315) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(348,413,315) x common factors =1 x 21 = 21
LCM(348,413,315) = ( 348 × 413 × 315 ) / 21
LCM(348,413,315) = 45273060 / 21
LCM(348,413,315) = 2155860
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FAQs on GCF of Fractions of 64/348, 42/413, 456/315
1. What is the HCF of 64,42,456?
The HCF of 64,42,456 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 64/348, 42/413, 456/315?
Answer: GCF of Numerators as per given numbers 64/348, 42/413, 456/315 is
GCF of Numerators i.e. for 64,42,456 is 2
LCM of denominators i.e. for 348,413,315 is 2155860.
Thus, GCF of Fractions is 2/2155860.Finally, GCF of Fractions for 64/348, 42/413, 456/315 is 2/2155860.