Question

Find the number of possible values of HCF, if the LCM of two numbers is 2007.​

Answer 1

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.

Answer 2

Step-by-step explanation:

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