Page 93 - Math Genius C4

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\ 30-Sep-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

Solution: (a) Divide 80 by 7. (b) Divide 144 by 12. common Factors
7 80 11 12 144 12 The numbers which are common among the factors of two or more numbers are
7 12
10 24 called the common factors. 1 × 12 = 12 1 × 30 = 30
7 24 Let us consider any two numbers, say 12 and 30.
3 0 Factors of 12 are 1 , 2 , 3 , 4, 6 and 12. 2 × 6 = 12 2 × 15 = 30

80 ÷ 7 = 11 R 3 144 ÷ 12 = 12 Factors of 30 are 1 , 2 , 3 , 5, 6 10, 15 and 30. 3 × 4 = 12 3 × 10 = 30

5 × 6 = 30
Since the division of 80 by 7 leaves the Since the division of 144 by 12 leaves no Here, we can see that factors 1, 2, 3 and 6 are present in both lists of factors.
remainder 3, 7 is not a factor of 80. remainder, 12 is a factor of 144.
So, 1, 2, 3 and 6 are the common factors of 12 and 30.
Properties of Factors Example: Find the common factors of: (a) 8 and 10. (b) 12 and 20.

1. Every number other than 1 has at least two factors: 1 and the number itself. Solution: (a) The factors of 8 are 1 , 2 , 4 and 8.
Examples: 2 = 1 × 2, so, 2 has 2 factors. The factors of 10 are 1 , 2 , 5 and 10.
3 = 1 × 3, so, 3 has 2 factors. So, the common factors of 8 and 10 are 1 and 2.
4 = 1 × 4 = 2 × 2, so, 4 has 3 factors. (b) The factors of 12 are 1 , 2 , 3, 4 , 6 and 12.

5 = 1 × 5, so, 5 has 2 factors, etc. The factors of 20 are 1 , 2 , 4 , 5, 10 and 20.
2. Every factor of a non-zero number is less than or equal to the number. So, the common factors of 12 and 20 are 1, 2, and 4.

3. Every number other than zero is a factor of itself. Also, the largest factor of a
number is the number itself. Practice time 5a
Examples: Factors of 8 are 1, 2, 4 and 8.

Factors of 18 are 1, 2, 3, 6, 9 and 18. 1. State whether the following statements are

It can easily be noted from the above numbers that the factors are true or false. Challenge Question
either less than or equal to the number. (a) Every number is the factor of itself. List all the common factors
Also, every number has one of its factors as the number itself. (b) 0 is a factor of every number. of 24 and 36. Choose one
pair of numbers that have
(c) 3 is a factor of 28.
4. A number has a finite (countable) number of factors. (d) The smallest factor of a number is the only 1 common factor. What
Examples: 23 = 1 × 23 has 2 factors (1 and 23). number itself. are such numbers called?

36 = 1 × 36; 2 × 18; 3 × 12; 4 × 9; 6 × 6 has 9 factors (1, 2, 3, 4, 6, 2. Use the multiplication method to list the factors of:
9, 12, 18 and 36). (a) 12 (b) 28 (c) 45 (d) 56 (e) 72

3. Use the division method to list the factors of:
Think Tank Logical Thinking
(a) 24 (b) 36 (c) 54 (d) 72 (e) 96
Social Emotional Learning
During a flood, the government evacuated 90 people trapped in a locality.
The rescue teams could arrange boats of different sizes. 4. Check whether the first number is a factor of the second number.
Fill in the following blanks to find different ways in which the people (a) 12, 140 (b) 10, 160 (c) 8, 176 (d) 15, 220
can be evacuated. 5. Find the common factors of the following pairs of numbers.
1. If there was just one boat, ________ people got into it. (a) 18 and 24 (b) 10 and 25 (c) 21 and 35 (d) 42 and 54
2. If there were two boats, ________ people got into each boat. (e) 60 and 90 (f) 24 and 32 (g) 18, 24 and 32
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 Teacher’s Discuss with the students, using examples, that every number is a factor of zero, but zero is not a factor of
required keeping in mind that no one is left behind. Tip any number.

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