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Q.

Find the HCF of 20, 24, 36.


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a

6

b

4

c

2

d

8 

answer is B.

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Detailed Solution

Here we are given numbers 20, 24, and 36.
Now let us find the factors of these three numbers one by one.
For 20,
We will first divide 20 by the smallest prime number which is 2, we get  202=10. Now we will divide 10 by the smallest prime number 2, which is 2, we get 102=5. 5 is also a prime number. So, prime factorisation of 20 looks like this:
Question ImageSo 20=2×2×5.
For 24,
Dividing 24 by smallest prime numbers which is 2 we get  242=12. Now dividing 12 by 2, we get  122=6. Again dividing 6 by 2 we get  62=3. 3 is prime number so, prime factorisation of 24 looks like this,
Question ImageSo, 24=2×2×2×3.
For 36,
Dividing 36 by 2 we get  362=18. Now dividing 18 by 2 we get 9. Now 9 will not get divided by 2 so the next prime number is 3. Dividing 9 by 3 we get  93=3. 3 is the prime number. So, prime factorisation of 36 looks like this
Question ImageSo, 36=2×2×3×3.
Now from the factorization of 20, 24, and 36, we can see common factors are 2,2.
So the highest common factor of 20, 24, 36 will be 2×2=4.
Hence 4 is the required HCF.
Now the greatest factor among these common factors is 4 so the highest common factor of 20, 24, and 36 is 4.
 
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