Find the HCF using Prime factorisation method 25 and 65
Answers
By using prime factorization method:
5l25
5
★Prime factor of 25 = 5 × 5 = 5²
5l65
13
★Prime factor of 65 = 5 × 13
Hence, the HCF of ( 25 and 65 ) = 5
Extra:
By using Euclid's division lemma [ Another method ]
★We know that for finding the HCF of two distinct positive integers a and b ( a > b ) and we obtain two integers q and r such that
a = b × q + r , 0 ≤ r < b
Step 1 :
25) 65 ( 2
50
----------------
15
65 = 25 × 2 + 15
Step 2 :
Remainder obtained in step ( 1 ) is 15 which is not zero.So, now will take 15 as divisor and 25 as dividend.
15) 25 ( 1
10
-----------
10
25 = 15 × 1 + 10
Step 3 :
Remainder obtained in step ( 2 ) is 10 which is not zero.Hence , now 10 will taken as divisor and 15 as dividend.
10) 15 ( 1
10
------------
5
15 = 10 × 1 + 5
Step 4 :
Remainder obtained in step ( 3 ) is 5 which is not zero. So, now will take 5 as divisor and 10 as dividend.
5) 10 ( 2
10
---------
0
10 = 5 × 2 + 0
Finally, we get remainder as zero .
Hence, HCF of ( 25, 65 ) is 5 because last divisor in solving this problem is 5 .
Answer:
Step-by-step explanation: