GCF of 162/32, 856/16, 689/21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 162/32, 856/16, 689/21 i.e 1/672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 162/32, 856/16, 689/21.
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 162/32,856/16,689/21?
Given fractions are 162/32,856/16,689/21
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 162/32,856/16,689/21, numerators are 162,856,689
Denominators are 32,16,21
The GCF of 162,856,689 is 1 .
LCM of 32,16,21 is 672.
The greatest common factor of 162/32,856/16,689/21 = [GCF of 162,856,689]/[LCM of 32,16,21]= 1/672
Therefore, the GCF of 162/32,856/16,689/21 is 1/672.
To find the highest common factor of 162,856,689, we have to find the factors of both numbers and list the highest common factor.
The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162
The factors of 856 are 1, 2, 4, 8, 107, 214, 428, 856
The factors of 689 are 1, 13, 53, 689
The HCF of 162,856,689 is 1.
Lets's calculate GCF of 162,856,689
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 162,856,689 By Matching Biggest Common Factor Method
Now, list down the factors of 162
:1,2,3,6,9,18,27,54,81,162
Now, list down the factors of 856
:1,2,4,8,107,214,428,856
Now, list down the factors of 689
:1,13,53,689
Greatest Common Factor
We found the factors 162,856,689 . The biggest common factor number is the GCF number.
So the greatest common factor 162,856,689 is 1.
Lets's calculate LCM of 32,16,21
| 2 | 32, 16, 21 |
| 2 | 16, 8, 21 |
| 2 | 4, 8, 21 |
| 2 | 2, 4, 21 |
| 1, 2, 21 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 1 x 2 x 21 = 672
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/672
Therefore, the GCF of Fractions 162/32,856/16,689/21 is 1/672
Least Common Multiple of 32,16,21 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 32,16,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,16,21) = 1
common factors(in case of two or more numbers have common factors) = 16
GCF(32,16,21) x common factors =1 x 16 = 16
LCM(32,16,21) = ( 32 × 16 × 21 ) / 16
LCM(32,16,21) = 10752 / 16
LCM(32,16,21) = 672
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FAQs on GCF of Fractions of 162/32, 856/16, 689/21
1. What is the HCF of 162,856,689?
The HCF of 162,856,689 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 162/32, 856/16, 689/21?
Answer: GCF of Numerators as per given numbers 162/32, 856/16, 689/21 is
GCF of Numerators i.e. for 162,856,689 is 1
LCM of denominators i.e. for 32,16,21 is 672.
Thus, GCF of Fractions is 1/672.Finally, GCF of Fractions for 162/32, 856/16, 689/21 is 1/672.