The H.C.F. of 24 and 40 is ___.

8, 
which is the largest number that divides both 24 and 40 completely.

True or False: The sum of the digits of a number must be divisible by 9 for the number to be divisible by 9.

True.

Fill in the blank: The formula to find the L.C.M. of two numbers is the product of the numbers divided by their ___.

H.C.F.

Find the H.C.F. of 18, 45, and 63.

• 18 = 2 × 3 × 3 = 2 × 3²

• 45 = 3 × 3 × 5 = 3² × 5

• 63 = 3 × 3 × 7 = 3² × 7

The common prime factor in all three numbers is 3, and the smallest power common to all is 3² = 9.

Fill in the blank: Co-prime numbers are two numbers whose H.C.F. is ___.

1.

True or False: All even numbers are prime.

False. The only even prime number is 2.

Calculate the L.C.M. of 8 and 12.

24, which is the smallest number that is a multiple of both 8 and 12.

Find the L.C.M. of 5, 6, and 15.

30, which is the smallest number that is a multiple of all three.

What is the relationship between H.C.F. and L.C.M. of two numbers?

The product of two numbers is equal to the product of their H.C.F. and L.C.M.

Fill in the blank: The prime factorization of 54 is ___.

2 × 3³.

True or False: A composite number has exactly three factors.

False. A composite number has more than two factors.