GCF of 72/724, 12/570, 906/362
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 72/724, 12/570, 906/362 i.e 6/206340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/724, 12/570, 906/362.
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 72/724,12/570,906/362?
Given fractions are 72/724,12/570,906/362
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 72/724,12/570,906/362, numerators are 72,12,906
Denominators are 724,570,362
The GCF of 72,12,906 is 6 .
LCM of 724,570,362 is 206340.
The greatest common factor of 72/724,12/570,906/362 = [GCF of 72,12,906]/[LCM of 724,570,362]= 6/206340
Therefore, the GCF of 72/724,12/570,906/362 is 6/206340.
To find the highest common factor of 72,12,906, we have to find the factors of both numbers and list the highest common factor.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 906 are 1, 2, 3, 6, 151, 302, 453, 906
The HCF of 72,12,906 is 6.
Lets's calculate GCF of 72,12,906
| 2 | 72, 12, 906 |
| 3 | 36, 6, 453 |
| 12, 2, 151 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 72,12,906 By Matching Biggest Common Factor Method
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 906
:1,2,3,6,151,302,453,906
Greatest Common Factor
We found the factors 72,12,906 . The biggest common factor number is the GCF number.
So the greatest common factor 72,12,906 is 6.
Lets's calculate LCM of 724,570,362
| 2 | 724, 570, 362 |
| 181 | 362, 285, 181 |
| 2, 285, 1 |
∴ So the LCM of the given numbers is 2 x 181 x 2 x 285 x 1 = 206340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/206340
Therefore, the GCF of Fractions 72/724,12/570,906/362 is 6/206340
Least Common Multiple of 724,570,362 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 724,570,362 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(724,570,362) = 2
common factors(in case of two or more numbers have common factors) = 362
GCF(724,570,362) x common factors =2 x 362 = 724
LCM(724,570,362) = ( 724 × 570 × 362 ) / 724
LCM(724,570,362) = 149390160 / 724
LCM(724,570,362) = 206340
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FAQs on GCF of Fractions of 72/724, 12/570, 906/362
1. What is the HCF of 72,12,906?
The HCF of 72,12,906 is 6
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 72/724, 12/570, 906/362?
Answer: GCF of Numerators as per given numbers 72/724, 12/570, 906/362 is
GCF of Numerators i.e. for 72,12,906 is 6
LCM of denominators i.e. for 724,570,362 is 206340.
Thus, GCF of Fractions is 6/206340.Finally, GCF of Fractions for 72/724, 12/570, 906/362 is 6/206340.