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\\December 6, 2023 12:53 PM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

Solution: (a) Divide 80 by 7. (b) Divide 144 by 12.

7 80 11 12 144 12
7 12
10 24
7 24
3 0

80 ÷ 7 = 11 R 3 144 ÷ 12 = 12
Since, the division of 80 by 7 leaves Since, the division of 144 by 12 leaves no

remainder 3, so 7 is not a factor of 80. remainder, so 12 is a factor of 144.

Factor Properties

1. Every number other than 1 has at least two factors: 1 and the number itself.
examples: 2 = 1 × 2, so, 2 has 2 factors.

3 = 1 × 3, so, 3 has 2 factors.
4 = 1 × 4, 2 × 2, so, 4 has 3 factors.
5 = 1 × 5, so, 5 has 2 factors, etc.

2. Every factor of a non-zero number is less than or equal to the number.
3. Every number other than zero is a factor of itself. Also, the largest factor of a

number is the number itself.
examples: Factors of 8 are 1, 2, 4 and 8.

Factors of 18 are 1, 2, 3, 6, 9 and 18.
It can easily be noted in above numbers that the factors are either
less than or equal to the number.

Also, every number has one of its factors as the number itself.

4. A number has finite (countable) number of factors.
examples: 23 = 1 × 23 has 2 factors (1 and 23).
36 = 1 × 36; 2 × 18; 3 × 12; 4 × 9; 6 × 6 has 9 factors (1, 2, 3, 4, 6,

9, 12, 18 and 36).

Think and Answer

During a flood, the government decided to evacuate 90 people trapped in
a locality. The rescue teams could arrange the boats of different sizes.
Fill in the following blanks to find different ways in which the people
can be evacuated.
1. If there was just one boat, ________ people got into it.
2. If there were two boats, ________ people got into it.
3. If there were 30 people in a boat, there were ________ boats required.
4. If a small boat has a maximum capacity of 12 people, then, ________ such boats would be
required keeping in mind that no one should be left behind.

90 Mathematics-4