GCF of 42/234, 312/316, 507/472
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 42/234, 312/316, 507/472 i.e 3/4362696 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/234, 312/316, 507/472.
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 42/234,312/316,507/472?
Given fractions are 42/234,312/316,507/472
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 42/234,312/316,507/472, numerators are 42,312,507
Denominators are 234,316,472
The GCF of 42,312,507 is 3 .
LCM of 234,316,472 is 4362696.
The greatest common factor of 42/234,312/316,507/472 = [GCF of 42,312,507]/[LCM of 234,316,472]= 3/4362696
Therefore, the GCF of 42/234,312/316,507/472 is 3/4362696.
To find the highest common factor of 42,312,507, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The factors of 507 are 1, 3, 13, 39, 169, 507
The HCF of 42,312,507 is 3.
Lets's calculate GCF of 42,312,507
| 3 | 42, 312, 507 |
| 14, 104, 169 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 42,312,507 By Matching Biggest Common Factor Method
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Now, list down the factors of 507
:1,3,13,39,169,507
Greatest Common Factor
We found the factors 42,312,507 . The biggest common factor number is the GCF number.
So the greatest common factor 42,312,507 is 3.
Lets's calculate LCM of 234,316,472
| 2 | 234, 316, 472 |
| 2 | 117, 158, 236 |
| 117, 79, 118 |
∴ So the LCM of the given numbers is 2 x 2 x 117 x 79 x 118 = 4362696
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/4362696
Therefore, the GCF of Fractions 42/234,312/316,507/472 is 3/4362696
Least Common Multiple of 234,316,472 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 234,316,472 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(234,316,472) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(234,316,472) x common factors =2 x 4 = 8
LCM(234,316,472) = ( 234 × 316 × 472 ) / 8
LCM(234,316,472) = 34901568 / 8
LCM(234,316,472) = 4362696
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FAQs on GCF of Fractions of 42/234, 312/316, 507/472
1. What is the HCF of 42,312,507?
The HCF of 42,312,507 is 3
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 42/234, 312/316, 507/472?
Answer: GCF of Numerators as per given numbers 42/234, 312/316, 507/472 is
GCF of Numerators i.e. for 42,312,507 is 3
LCM of denominators i.e. for 234,316,472 is 4362696.
Thus, GCF of Fractions is 3/4362696.Finally, GCF of Fractions for 42/234, 312/316, 507/472 is 3/4362696.