What is the definition of the Highest Common Factor (HCF)?

The Highest Common Factor (HCF) of two or more numbers is the largest number that divides each of them without leaving a remainder. 

For Example, 

The HCF of 12 and 18 is 6

How do you calculate the Least Common Multiple (LCM) of two numbers?

To calculate the Least Common Multiple (LCM) of two numbers, you can use the formula: 

LCM(a, b) = (a x b)/ HCF(a, b)

This method finds the LCM by first determining the HCF.

Find the HCF and LCM of the numbers 24 and 36.

(Hint: Start by listing the factors)

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. 

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. 

The HCF is 12 and the LCM is 72, calculated as

(24 x 36) / 12 

= 72.

If two numbers are 45 and 60, what is their HCF using the prime factorization method?

The prime factorization of 45 is 3² x 5, and for 60, it is 2² x 3 x 5. 

The common prime factors are 3 and 5, so the HCF = 3¹ x 5¹ = 15.

What is the relationship between HCF and LCM for any two numbers a and b?

The relationship is given by the equation: 

HCF(a, b) x LCM(a, b) = a x b. 

This means that the product of the HCF and LCM of two numbers is equal to the product of the numbers themselves.

What is a quick method to find the LCM of multiple numbers?

A quick method to find the LCM of multiple numbers is to use the prime factorization of each number and take the highest power of each prime that appears in any of the factorizations.

Calculate the HCF and LCM of 8 and 12.

(Hint: Use the prime factorization method)

The prime factorization of 8 is 2³, and for 12, 

it is 2² x 3. 

The HCF is 2² = 4, and the LCM is 2³ x 3 = 24.

Find the HCF and LCM of the numbers 24 and 36.

(Hint: Start by listing the factors)

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. 

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The HCF is 12 and the LCM is 72, calculated as (24 x 36) / 12 = 72.

If two numbers are 45 and 60, what is their HCF using the prime factorization method?

The prime factorization of 45 is 3² x 5, and for 60, it is 2² x 3 x 5. 

The common prime factors are 3 and 5, so the HCF = 3¹ x 5¹ = 15.