GCF of 290/78, 725/148
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 290/78, 725/148 i.e 145/5772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 290/78, 725/148.
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 290/78,725/148?
Given fractions are 290/78,725/148
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 290/78,725/148, numerators are 290,725
Denominators are 78,148
The GCF of 290,725 is 145 .
LCM of 78,148 is 5772.
The greatest common factor of 290/78,725/148 = [GCF of 290,725]/[LCM of 78,148]= 145/5772
Therefore, the GCF of 290/78,725/148 is 145/5772.
To find the highest common factor of 290,725, we have to find the factors of both numbers and list the highest common factor.
The factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290
The factors of 725 are 1, 5, 25, 29, 145, 725
The HCF of 290,725 is 145.
Lets's calculate GCF of 290,725
| 5 | 290, 725 |
| 29 | 58, 145 |
| 2, 5 |
∴ So the GCF of the given numbers is 5 x 29 = 145
Greatest Common Factor of 290,725 By Matching Biggest Common Factor Method
Now, list down the factors of 290
:1,2,5,10,29,58,145,290
Now, list down the factors of 725
:1,5,25,29,145,725
Greatest Common Factor
We found the factors 290,725 . The biggest common factor number is the GCF number.
So the greatest common factor 290,725 is 145.
Lets's calculate LCM of 78,148
| 2 | 78, 148 |
| 39, 74 |
∴ So the LCM of the given numbers is 2 x 39 x 74 = 5772
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 145/5772
Therefore, the GCF of Fractions 290/78,725/148 is 145/5772
Least Common Multiple of 78,148 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 78,148 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,148) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(78,148) x common factors =2 x 1 = 2
LCM(78,148) = ( 78 × 148 ) / 2
LCM(78,148) = 11544 / 2
LCM(78,148) = 5772
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FAQs on GCF of Fractions of 290/78, 725/148
1. What is the HCF of 290,725?
The HCF of 290,725 is 145
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 290/78, 725/148?
Answer: GCF of Numerators as per given numbers 290/78, 725/148 is
GCF of Numerators i.e. for 290,725 is 145
LCM of denominators i.e. for 78,148 is 5772.
Thus, GCF of Fractions is 145/5772.Finally, GCF of Fractions for 290/78, 725/148 is 145/5772.