GCF of 64/144, 589/701, 509/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 64/144, 589/701, 509/420 i.e 1/3533040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 64/144, 589/701, 509/420.
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 64/144,589/701,509/420?
Given fractions are 64/144,589/701,509/420
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 64/144,589/701,509/420, numerators are 64,589,509
Denominators are 144,701,420
The GCF of 64,589,509 is 1 .
LCM of 144,701,420 is 3533040.
The greatest common factor of 64/144,589/701,509/420 = [GCF of 64,589,509]/[LCM of 144,701,420]= 1/3533040
Therefore, the GCF of 64/144,589/701,509/420 is 1/3533040.
To find the highest common factor of 64,589,509, we have to find the factors of both numbers and list the highest common factor.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 589 are 1, 19, 31, 589
The factors of 509 are 1, 509
The HCF of 64,589,509 is 1.
Lets's calculate GCF of 64,589,509
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 64,589,509 By Matching Biggest Common Factor Method
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 589
:1,19,31,589
Now, list down the factors of 509
:1,509
Greatest Common Factor
We found the factors 64,589,509 . The biggest common factor number is the GCF number.
So the greatest common factor 64,589,509 is 1.
Lets's calculate LCM of 144,701,420
| 2 | 144, 701, 420 |
| 2 | 72, 701, 210 |
| 3 | 36, 701, 105 |
| 12, 701, 35 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 12 x 701 x 35 = 3533040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3533040
Therefore, the GCF of Fractions 64/144,589/701,509/420 is 1/3533040
Least Common Multiple of 144,701,420 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 144,701,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(144,701,420) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(144,701,420) x common factors =1 x 12 = 12
LCM(144,701,420) = ( 144 × 701 × 420 ) / 12
LCM(144,701,420) = 42396480 / 12
LCM(144,701,420) = 3533040
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FAQs on GCF of Fractions of 64/144, 589/701, 509/420
1. What is the HCF of 64,589,509?
The HCF of 64,589,509 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 64/144, 589/701, 509/420?
Answer: GCF of Numerators as per given numbers 64/144, 589/701, 509/420 is
GCF of Numerators i.e. for 64,589,509 is 1
LCM of denominators i.e. for 144,701,420 is 3533040.
Thus, GCF of Fractions is 1/3533040.Finally, GCF of Fractions for 64/144, 589/701, 509/420 is 1/3533040.