The number 10
10 is a triangular number: 1 + 2 + … + 4 = 10. Its prime factorisation is 2 × 5. Divisors (4): 1, 2, 5, 10.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10: a triangular number: 1 + 2 + … + 4 = 10; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 1; a semiprime: 2 × 5, the product of two primes.
- 2
10 is composite. Its prime factorisation is
- 3
The divisors add up to 18; without 10 itself that is 8, so 10 is deficient (8 is less than 10). Euler's totient φ(10) = 4 numbers up to 10 share no factor with it.
- 4
The digits of 10 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 6 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10 = 2 \times 5 \]
10 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 4 |
| Sum of divisors | 18 |
| Euler totient φ(n) | 4 |
| Square | 100 |
| Cube | 1000 |
| Square root | 3.162278 |
| Digit sum / digital root | 1 / 1 |
| Collatz steps to 1 | 6 |
| Scientific notation | 1 × |
10 in other forms
| Form | Value |
|---|---|
| In words | ten |
| Roman numerals | X |
| Binary (base 2) | 1010 |
| Octal (base 8) | 12 |
| Hexadecimal (base 16) | A |
| Base 3 | 101 |
| As time | 10 seconds |
Is 10 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10 ÷ 2 = 5) | 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 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10 ÷ 5 = 2) | 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 3) | 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 2) | 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 (10 ÷ 10 = 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10 a prime number?
No. 10 = 2 × 5, so it is divisible by 2.
What are the factors of 10?
1, 2, 5, 10.
What is 10 in binary?
1010 (hexadecimal A, octal 12).
What is the square root of 10?
About 3.1623.
What is 10 in Roman numerals?
X.
Is 10 divisible by 3?
No. Its digits add up to 1, which is not a multiple of 3.
What is special about the number 10?
10 is a triangular number: 1 + 2 + … + 4 = 10; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 1; a semiprime: 2 × 5, the product of two primes.