Divisors of Natural Numbers
Welcome to an exciting journey into the world of divisors! Understanding divisors helps us see how numbers are connected and how they can be broken apart.
What is a Divisor?
Definition: If a natural number a can be divided by natural number b with no remainder (exactly), then b is called a divisor of a.
Example:
12 ÷ 3 = 4 (exact division, no remainder)
So 3 is a divisor of 12
Notation: We write b | a to mean "b divides a" or "b is a divisor of a"
Example: 3 | 12 means "3 divides 12"
Example: 3 | 12 means "3 divides 12"
Every Number Has Divisors
Important Facts:
- 1 divides every natural number
- Every number divides itself
- So every natural number has at least two divisors: 1 and itself
Example: Divisors of 7 are 1 and 7
Because: 7 ÷ 1 = 7 ✓ and 7 ÷ 7 = 1 ✓