Page 64 - ICSE Math 5

Properties of Factors Properties of Multiples

• The smallest factor of every number is 1. • Every number is a multiple of 1 and itself.
• Every number is the greatest factor of • Every multiple of a number is exactly
itself. divisible by that particular number.

• A number can have only a limited number • A number can have unlimited multiples.
of factors. Every number except 1 can have
at least two factors: 1 and the number itself.
• The factors of a number are always smaller • The multiples of a number are either
than or equal to that number. greater than or equal to that number.

Let’s revise the types of numbers that we have studied in the previous class.
• Even numbers are the multiples of 2 ending with the digits 0, 2, 4, 6 and 8. Numbers such
as 10, 12, 20, 364, 982 and 356 are some even numbers.
• Odd numbers are the numbers ending with the digits 1, 3, 5, 7 and 9. Numbers such as 11,
13, 31, 463, 285 and 299 are some odd numbers.

• Prime numbers are the numbers having only two factors which are 1 and the number itself.
For example, 2, 3, 7, 11, 13 and 17 are some prime numbers.
• Composite numbers are the numbers having more than two factors. They can be divided
exactly by their factors. Some examples of composite numbers are 6, 8, 12, 15, 20 and 24.

• Twin primes are the pairs of prime numbers having a difference of 2 in between them. For
example, (3, 5); (5, 7); (11, 13); (17, 19) and (29, 31) are some twin prime pairs.
• Co-prime numbers are numbers which do not have any common factor except 1. All prime
numbers are co-prime to each other.

Example 8: Look at the list of numbers from 1 to 30 and find out the twin prime pairs.
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30

Solution: All the prime numbers between 1 and 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
 Twin prime pairs are (3, 5); (5, 7); (11, 13) and (17, 19).
Example 9: Show that 21 and 32 are co-prime numbers.
Solution: Using factor tree method, write the factors of 21 and 32.

21 32

3 × 7 4 × 8

2 × 2 2 × 4

2 × 2
21 = 3 × 7 32 = 2 × 2 × 2 × 2 × 2

We see that 21 and 32 have no common factor except 1. Thus, 21 and 32 are
co-prime numbers.
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