GCF of 702/54, 507/234
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 702/54, 507/234 i.e 39/702 easily. The following is the detailed procedure to determine the greatest common factor of fractions 702/54, 507/234.
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 702/54,507/234?
Given fractions are 702/54,507/234
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 702/54,507/234, numerators are 702,507
Denominators are 54,234
The GCF of 702,507 is 39 .
LCM of 54,234 is 702.
The greatest common factor of 702/54,507/234 = [GCF of 702,507]/[LCM of 54,234]= 39/702
Therefore, the GCF of 702/54,507/234 is 39/702.
To find the highest common factor of 702,507, we have to find the factors of both numbers and list the highest common factor.
The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702
The factors of 507 are 1, 3, 13, 39, 169, 507
The HCF of 702,507 is 39.
Lets's calculate GCF of 702,507
| 3 | 702, 507 |
| 13 | 234, 169 |
| 18, 13 |
∴ So the GCF of the given numbers is 3 x 13 = 39
Greatest Common Factor of 702,507 By Matching Biggest Common Factor Method
Now, list down the factors of 702
:1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702
Now, list down the factors of 507
:1,3,13,39,169,507
Greatest Common Factor
We found the factors 702,507 . The biggest common factor number is the GCF number.
So the greatest common factor 702,507 is 39.
Lets's calculate LCM of 54,234
| 2 | 54, 234 |
| 3 | 27, 117 |
| 3 | 9, 39 |
| 3, 13 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 13 = 702
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 39/702
Therefore, the GCF of Fractions 702/54,507/234 is 39/702
Least Common Multiple of 54,234 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 54,234 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,234) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(54,234) x common factors =18 x 1 = 18
LCM(54,234) = ( 54 × 234 ) / 18
LCM(54,234) = 12636 / 18
LCM(54,234) = 702
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FAQs on GCF of Fractions of 702/54, 507/234
1. What is the HCF of 702,507?
The HCF of 702,507 is 39
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 702/54, 507/234?
Answer: GCF of Numerators as per given numbers 702/54, 507/234 is
GCF of Numerators i.e. for 702,507 is 39
LCM of denominators i.e. for 54,234 is 702.
Thus, GCF of Fractions is 39/702.Finally, GCF of Fractions for 702/54, 507/234 is 39/702.