EXERCISE 1.3

1. List the factors of 27 and 36 and then find the HC
   2.- ad Write the first five multiples of 6 and 8 .
   b) What is the LCM of 6 and 8 ?
2. a a List the prime numbers up to 40 .
   b) Is 57 a prime number? Explain.

1. Factors and Highest Common Factor (HCF)

• The factors of 27 are: 1, 3, 9, 27.

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

• The common factors of 27 and 36 are: 1, 3, 9.
• The highest common factor (HCF) is the largest of these common factors, which is 9.

2. Multiples and Least Common Multiple (LCM)

• The first five multiples of 6 are: 6, 12, 18, 24, 30.

• The first five multiples of 8 are: 8, 16, 24, 32, 40.

• The multiples of 6 are: 6, 12, 18, 24, 30, …
• The multiples of 8 are: 8, 16, 24, 32, 40, …
• The least common multiple (LCM) is the smallest multiple that appears in both lists, which is 24.

3. Prime Numbers

• The prime numbers up to 40 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.

• A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
• The factors of 57 are: 1, 3, 19, 57.
• Since 57 has divisors other than 1 and itself (specifically, 3 and 19), it is not a prime number.

Summary of Answers:

1. HCF of 27 and 36 is 9.
2. a. First five multiples of 6: 6, 12, 18, 24, 30; First five multiples of 8: 8, 16, 24, 32, 40.
   b. LCM of 6 and 8 is 24.
3. a. Prime numbers up to 40: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.
   b. 57 is not a prime number.