Find all factors of 6.

Solution

Divide 6 by each number starting from 1:

• $6 \div 1 = 6$ → 1 is a factor
• $6 \div 2 = 3$ → 2 is a factor
• $6 \div 3 = 2$ → 3 is a factor
• $6 \div 4 = 1$ remainder 2 → 4 is NOT a factor
• $6 \div 5 = 1$ remainder 1 → 5 is NOT a factor
• $6 \div 6 = 1$ → 6 is a factor

The factors of 6 are: 1, 2, 3, and 6

Find all factors of 45.

Solution

Write 45 as a product of two numbers:

• $1 \times 45 = 45$ → factors: 1 and 45
• $3 \times 15 = 45$ → factors: 3 and 15
• $5 \times 9 = 45$ → factors: 5 and 9

The factors of 45 are: 1, 3, 5, 9, 15, and 45

Find all factors of 36.

Solution

• $36 \div 1 = 36$
• $36 \div 2 = 18$
• $36 \div 3 = 12$
• $36 \div 4 = 9$
• $36 \div 5 = 7$ remainder 1 → stop checking
• $36 \div 6 = 6$

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36

A multiple of a number is the product of that number and any counting number (1, 2, 3, 4, 5...).

When we say "multiples of 5", we mean: 5, 10, 15, 20, 25, 30, and so on.

How to Find Multiples of a Number

Step 1: Multiply the number by 1, then by 2, then by 3, and continue.

Step 2: Each result is a multiple of that number.

Step 3: The list continues forever unless we set a limit.

Write the first five multiples of 7.

Solution

• $7 \times 1 = 7$
• $7 \times 2 = 14$
• $7 \times 3 = 21$
• $7 \times 4 = 28$
• $7 \times 5 = 35$

The first five multiples of 7 are: 7, 14, 21, 28, and 35

Write all multiples of 4 between 2 and 30.

Solution

List multiples of 4:

• $4 \times 1 = 4$
• $4 \times 2 = 8$
• $4 \times 3 = 12$
• $4 \times 4 = 16$
• $4 \times 5 = 20$
• $4 \times 6 = 24$
• $4 \times 7 = 28$
• $4 \times 8 = 32$ (too big)

The multiples of 4 between 2 and 30 are: 4, 8, 12, 16, 20, 24, and 28

• Factors go into a number (division). A finite list.
• Multiples come from a number (multiplication). An infinite list.
• 1 is a factor of every number.
• Every number is a factor of itself.
• Every number is a multiple of 1 and of itself.
• The smallest multiple of any number is the number itself ($n \times 1 = n$).

In Tanzania, knowing factors and multiples helps in everyday situations. For example, if a shopkeeper has 24 mangoes and wants to pack them into equal groups for sale, factors help determine how many mangoes can go in each bag with none left over — such as 6 bags of 4 mangoes each, or 4 bags of 6 mangoes each. This is useful when dividing items for sale, sharing food among family members, or arranging objects in equal rows during school events or market days.