The number 100
100 is a perfect square (10²). Its prime factorisation is × . Divisors (9): 1, 2, 4, 5, 10, 20, 25, 50, 100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 100: a perfect square (10²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 1.
- 2
100 is composite. Its prime factorisation is
- 3
The divisors add up to 217; without 100 itself that is 117, so 100 is abundant (117 is more than 100). Euler's totient φ(100) = 40 numbers up to 100 share no factor with it.
- 4
The digits of 100 add up to 1, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 25 steps to reach 1.
LaTeX source of the formulas on this page
\[ 100 = 2^{2} \times 5^{2} \]100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 9 |
| Sum of divisors | 217 |
| Euler totient φ(n) | 40 |
| Square | 10000 |
| Cube | 1000000 |
| Square root | 10 |
| Digit sum / digital root | 1 / 1 |
| Collatz steps to 1 | 25 |
| Scientific notation | 1 × |
| Perfect power |
100 in other forms
| Form | Value |
|---|---|
| In words | one hundred |
| Roman numerals | C |
| Binary (base 2) | 1100100 |
| Octal (base 8) | 144 |
| Hexadecimal (base 16) | 64 |
| Base 3 | 10201 |
| As time | 100 seconds = 1 min 40 s |
Is 100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (100 ÷ 2 = 50) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (100 ÷ 4 = 25) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (100 ÷ 5 = 20) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (100 ÷ 10 = 10) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 100 a prime number?
No. 100 = × , so it is divisible by 2.
What are the factors of 100?
1, 2, 4, 5, 10, 20, 25, 50, 100.
What is 100 in binary?
1100100 (hexadecimal 64, octal 144).
What is the square root of 100?
10, because 10 × 10 = 100.
What is 100 in Roman numerals?
C.
Is 100 divisible by 3?
No. Its digits add up to 1, which is not a multiple of 3.
What is special about the number 100?
100 is a perfect square (10²); a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 1.