GCF of 1024/82, 9632/909
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1024/82, 9632/909 i.e 32/74538 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1024/82, 9632/909.
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 1024/82,9632/909?
Given fractions are 1024/82,9632/909
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 1024/82,9632/909, numerators are 1024,9632
Denominators are 82,909
The GCF of 1024,9632 is 32 .
LCM of 82,909 is 74538.
The greatest common factor of 1024/82,9632/909 = [GCF of 1024,9632]/[LCM of 82,909]= 32/74538
Therefore, the GCF of 1024/82,9632/909 is 32/74538.
To find the highest common factor of 1024,9632, we have to find the factors of both numbers and list the highest common factor.
The factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024
The factors of 9632 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 43, 56, 86, 112, 172, 224, 301, 344, 602, 688, 1204, 1376, 2408, 4816, 9632
The HCF of 1024,9632 is 32.
Lets's calculate GCF of 1024,9632
| 2 | 1024, 9632 |
| 2 | 512, 4816 |
| 2 | 256, 2408 |
| 2 | 128, 1204 |
| 2 | 64, 602 |
| 32, 301 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Greatest Common Factor of 1024,9632 By Matching Biggest Common Factor Method
Now, list down the factors of 1024
:1,2,4,8,16,32,64,128,256,512,1024
Now, list down the factors of 9632
:1,2,4,7,8,14,16,28,32,43,56,86,112,172,224,301,344,602,688,1204,1376,2408,4816,9632
Greatest Common Factor
We found the factors 1024,9632 . The biggest common factor number is the GCF number.
So the greatest common factor 1024,9632 is 32.
Lets's calculate LCM of 82,909
Given numbers has no common factors except 1. So, there LCM is their product i.e 74538
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/74538
Therefore, the GCF of Fractions 1024/82,9632/909 is 32/74538
Least Common Multiple of 82,909 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 82,909 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,909) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(82,909) x common factors =1 x 1 = 1
LCM(82,909) = ( 82 × 909 ) / 1
LCM(82,909) = 74538 / 1
LCM(82,909) = 74538
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FAQs on GCF of Fractions of 1024/82, 9632/909
1. What is the HCF of 1024,9632?
The HCF of 1024,9632 is 32
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 1024/82, 9632/909?
Answer: GCF of Numerators as per given numbers 1024/82, 9632/909 is
GCF of Numerators i.e. for 1024,9632 is 32
LCM of denominators i.e. for 82,909 is 74538.
Thus, GCF of Fractions is 32/74538.Finally, GCF of Fractions for 1024/82, 9632/909 is 32/74538.