Maths Form 1 Chapter 2 Number Patterns And Sequences

• 2.1 Number Sequences

 1. A number sequences is an arrangement of numbers according to a set pattern.

2. Example of number sequences are:

• 2, 4, 6, 8, 10 …
• 5, 10, 15, 20 …
• 1, 4, 7, 10, 13 …
• 10, 8, 6, 4 …

 3.We can extend number sequences or complete missing term in number sequences if we know the patterns in the number sequences.

 4. We can construct number sequences based on given patterns.

• 2. 2 Odd and Even Number

1, 3, 5, 7, 9, 11, 13 …

1. The number above is a list of odd numbers.

 All odd numbers cannot be divided by 2 without any remainder.

2, 4, 6, 8, 10, 12 …

1. The number above is a list of even number.

 All even numbers can be divided by 2 without any remainder.

• 2.3 Prime Numbers

1. A prime number is a whole number that can only be divided by 1 and itself without any remainder.

2. The whole number 0 and 1 are not prime numbers.

 3. 2 is the smallest prime number.

 4. Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

• 2.4 Multiples of Whole Numbers

 1.The multiples of a whole number can be obtained by multiplying the whole number with another whole number other than zero.

 2. A number is a multiple of a given number if the number can be divided by the given number.

• 2.5 Common Multiples of Whole Numbers

 1. Common multiples of two or more whole numbers are multiples of each of those whole numbers.

 2. For example, the multiples of 2 are 2, 4, 6, 8, 10, 12, 14 …

 3. The multiples of 3 are 3, 6, 9, 12, 15 …

 4. Thus, the common multiple of 2 and 3 are 6, 12 …

•  2.6 Lowest Common Multiple (LCM) of Whole Numbers

 1. The lowest common multiples (LCM) of two or more whole numbers are multiples of each of those whole numbers.

 2. For example, 6, 12 … are common multiples of 2 and 3. 6 have the smallest value. Thus, 6 is the LCM of 2 and 3.

 3. LCM can be found by repeated division by prime number such as 2, 3, 5, 7, 11 …

Example: Find the LCM of 4 and 9,

(1)  Divide 4 by prime number 2. Bring down 9 because it cannot be divided by 2. (2)  Divide 2 by prime number 2. Bring down 9 because it cannot be divided by 2. (3)  Divide 9 by prime number 3. (4)  Divide 3 by prime number 3. (5)  Stop when all the number became 1.

= The LCM of 4 and 9 is 36.

• 2.7 Factors of Whole Numbers

 1. A factor of a whole number is a number that ca divide the whole number without any remainder.

 2. For example, 12 can be divided by 1, 2, 3, 4, 6, and 12 without any remainder.

 3. Thus, 1, 2, 3, 4, 6 and 12 are factors of 12.

• 2.8 Prime Factors of Whole Numbers

 1. A prime factor is a prime number which is a factor of a whole number.

 2. For example, the factors of 14 are 1, 2, 7, and 14. 2 and 7 are prime numbers. Thus, 2 and 7 are prime factors of 14.

• 2.9 Common Factor of Whole Numbers

 1. Common factors of two or more whole numbers are factors of each of those numbers.

Example: Find the common factor of 12 and 18.

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

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

Thus, the common factor of 12and 18 are 1, 2, 3 and 6.

• 2.10 Highest Common Factor (HCF) of Whole Numbers

 1. The HCF of whole numbers can be found by doing repeated division with prime number starting with 2, 3, 5, 7, …

Example: Find the HCF of 12 and 18.

(1)  Divide 12 and 18 by the common prime factor 2. (2)  Divide 6 and 9 by the common prime factor 3. (3)  Stop the division because 2 and 3 do not have any common prime factor.