I collected 10 sunflowers from the garden and want to arrange them in rows and columns. The document then provides information on factors and multiples: Factors are numbers that are exactly divisible by another number. To find factors, start with 1 x Number and try dividing by other numbers. Repeated factors or those that are doubles indicate you have found all the factors. Multiples are results of multiplying a number by counting numbers like 1, 2, 3, etc. A number has unlimited multiples. The document provides examples of finding factors and multiples and exercises for the reader to complete.

2. I collected 10 sunflowers from the garden, want to arrange them on my table in
Rows and columns. Please HELP!

3. Factors are the numbers which when multiplied will give us another number

4. To check weather the given number is factor of another number or not,
we have to check weather the latter number is exactly divisible by given number or not.
For example :- 15 ÷ 5 = 3 and 15 ÷ 3 =5

5. We can find all the factors of a given numbers in two ways :-
1. By Multiplication
2. By Division
Let us find all the factors of 15 by Multiplication and Division as well
By Multiplication By Division
1 x 15 = 15
3 X 5 = 15
15 ÷ 1 = 15
15 ÷ 3 = 5
15 ÷ 5 = 3
15 ÷ 15 =1
Thus , 1,3,5 and 15 all are the factors of 15

6. Finding Factors
Step 1 : Start with 1 x Number
Step 2 : Try with 2, 3,4 etc
Step 3: when you repeat your Factors, cross out the repeats- you are done
at this point
Step 4 :- If you get doubles(Such as 4 x 4 ), then you are done .
Repeats or Doubles let’s you know you are done.
What are the factors of 16?

7.  1 is a factor of each number and is called universal factor.
1 is a smallest factor
 Number is a factor of itself. Greatest factor of a number is
number itself.
 All the factors of a number are between 1 and number.
 All the numbers are factors of zero.

8. Method 1: By finding common Factors
Number 1: 20 -1,2,4,5,10,20
Number 2:40 – 1,2,4,5,8,10,20,40
Common factors – 1,2,4,5,10,20
Highest common factor - 20

9. Method 2: By prime factorization
Number1: 84 =2 X 2X 3X7X1
Number 2: 72= 2 x2x 2x3x3x1
Common Factors 2x2x3x1
HCF - 12

10. Method 3: Long Division Method
Number1: 72
Number2 :90

11. Multiples :- A multiple is a result of multiplying a
number by counting numbers like – 1,2,3 and so on
A number can have unlimited multiples.

12. Write first 5 multiples of 17
17 x 1 = 17
17 x 2 = 34
17 x 3 = 51
17 x 4 = 68
17 x 5 = 85
Thus, first 5 multiples of 17 are 17,34,51,68 and 85

14. EXERCISE 3.1
1. Write all the factors of the following numbers :
(a) 24 (b) 15 (c) 21
(d) 27 (e) 12 (f) 20
(g) 18 (h) 23 (i) 36
2. Write first five multiples of :
(a) 5 (b) 8 (c) 9
3. Match the items in column 1 with the items in column 2.
Column 1 Column 2
(i) 35 (a) Multiple of 8
(ii) 15 (b) Multiple of 7
(iii) 16 (c) Multiple of 70
(iv) 20 (d) Factor of 30
(v) 25 (e) Factor of 50
(f) Factor of 20
4. Find all the multiples of 9 upto 100.

15. The numbers which have only two factors, 1 and number itself are called
Prime Numbers.
Examples:- 2,3,5,7 and 11 are all prime numbers.

16. The numbers(except 1) which are not prime are called composite numbers.
Composite Numbers always has more than two factors.
Example 4