GCF of 249/54, 688/25, 380/84
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 249/54, 688/25, 380/84 i.e 1/18900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 249/54, 688/25, 380/84.
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 249/54,688/25,380/84?
Given fractions are 249/54,688/25,380/84
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 249/54,688/25,380/84, numerators are 249,688,380
Denominators are 54,25,84
The GCF of 249,688,380 is 1 .
LCM of 54,25,84 is 18900.
The greatest common factor of 249/54,688/25,380/84 = [GCF of 249,688,380]/[LCM of 54,25,84]= 1/18900
Therefore, the GCF of 249/54,688/25,380/84 is 1/18900.
To find the highest common factor of 249,688,380, we have to find the factors of both numbers and list the highest common factor.
The factors of 249 are 1, 3, 83, 249
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
The HCF of 249,688,380 is 1.
Lets's calculate GCF of 249,688,380
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 249,688,380 By Matching Biggest Common Factor Method
Now, list down the factors of 249
:1,3,83,249
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Now, list down the factors of 380
:1,2,4,5,10,19,20,38,76,95,190,380
Greatest Common Factor
We found the factors 249,688,380 . The biggest common factor number is the GCF number.
So the greatest common factor 249,688,380 is 1.
Lets's calculate LCM of 54,25,84
| 2 | 54, 25, 84 |
| 3 | 27, 25, 42 |
| 9, 25, 14 |
∴ So the LCM of the given numbers is 2 x 3 x 9 x 25 x 14 = 18900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18900
Therefore, the GCF of Fractions 249/54,688/25,380/84 is 1/18900
Least Common Multiple of 54,25,84 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 54,25,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,25,84) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(54,25,84) x common factors =1 x 6 = 6
LCM(54,25,84) = ( 54 × 25 × 84 ) / 6
LCM(54,25,84) = 113400 / 6
LCM(54,25,84) = 18900
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FAQs on GCF of Fractions of 249/54, 688/25, 380/84
1. What is the HCF of 249,688,380?
The HCF of 249,688,380 is 1
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 249/54, 688/25, 380/84?
Answer: GCF of Numerators as per given numbers 249/54, 688/25, 380/84 is
GCF of Numerators i.e. for 249,688,380 is 1
LCM of denominators i.e. for 54,25,84 is 18900.
Thus, GCF of Fractions is 1/18900.Finally, GCF of Fractions for 249/54, 688/25, 380/84 is 1/18900.