GCF of 720/28, 465/462
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 720/28, 465/462 i.e 15/924 easily. The following is the detailed procedure to determine the greatest common factor of fractions 720/28, 465/462.
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 720/28,465/462?
Given fractions are 720/28,465/462
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 720/28,465/462, numerators are 720,465
Denominators are 28,462
The GCF of 720,465 is 15 .
LCM of 28,462 is 924.
The greatest common factor of 720/28,465/462 = [GCF of 720,465]/[LCM of 28,462]= 15/924
Therefore, the GCF of 720/28,465/462 is 15/924.
To find the highest common factor of 720,465, we have to find the factors of both numbers and list the highest common factor.
The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
The factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465
The HCF of 720,465 is 15.
Lets's calculate GCF of 720,465
| 3 | 720, 465 |
| 5 | 240, 155 |
| 48, 31 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 720,465 By Matching Biggest Common Factor Method
Now, list down the factors of 720
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720
Now, list down the factors of 465
:1,3,5,15,31,93,155,465
Greatest Common Factor
We found the factors 720,465 . The biggest common factor number is the GCF number.
So the greatest common factor 720,465 is 15.
Lets's calculate LCM of 28,462
| 2 | 28, 462 |
| 7 | 14, 231 |
| 2, 33 |
∴ So the LCM of the given numbers is 2 x 7 x 2 x 33 = 924
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/924
Therefore, the GCF of Fractions 720/28,465/462 is 15/924
Least Common Multiple of 28,462 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 28,462 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,462) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(28,462) x common factors =14 x 1 = 14
LCM(28,462) = ( 28 × 462 ) / 14
LCM(28,462) = 12936 / 14
LCM(28,462) = 924
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FAQs on GCF of Fractions of 720/28, 465/462
1. What is the HCF of 720,465?
The HCF of 720,465 is 15
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 720/28, 465/462?
Answer: GCF of Numerators as per given numbers 720/28, 465/462 is
GCF of Numerators i.e. for 720,465 is 15
LCM of denominators i.e. for 28,462 is 924.
Thus, GCF of Fractions is 15/924.Finally, GCF of Fractions for 720/28, 465/462 is 15/924.