Find the number of possible values of HCF, if the LCM of two numbers is 2007.
Answers
Finding LCM and HCF
Given: The LCM of two numbers is 2007
To find: The number of possible values of HCF
Solution:
First we prime factorise the LCM 2007.
2007 = 3 × 669
2007 = 3 × 3 × 223
Another number can be found,
2007 = 1 × 3 × 3 × 223
From above, we can conclude that the pairs (1, 2007), (3, 2007), (9, 2007), (223, 2007), (669, 2007) and (2007, 2007) have LCM = 2007.
Now we proceed to find HCF of the given pairs.
- HCF(1, 2007) = 1
- HCF(3, 2007) = 3
- HCF(9, 2007) = 9
- HCF(223, 2007) = 223
- HCF(669, 2007) = 669
- HCF(2007, 2007) = 2007
Answer: The possibility values of HCF are 1, 3, 9, 223, 669 and 2007.
Step-by-step explanation:
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