Page 92 - Math Genius C4

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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 the Since the division of 144 by 12 leaves no

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

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 from the 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 a 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 Tank Logical Thinking
Social Emotional Learning
During a flood, the government evacuated 90 people trapped in a locality.
The rescue teams could arrange 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 each boat.
3. If there were 30 people in a boat, there were ________ boats.
4. If a small boat has a maximum capacity of 12 people, then, ________ such boats would be
required keeping in mind that no one is left behind.

90 Mathematics-4