The number 252
252 is a palindrome: it reads 252 backwards too. Its prime factorisation is × × 7. Divisors (18): 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84 … 252.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 252: a palindrome: it reads 252 backwards too; a Harshad number: divisible by its digit sum 9.
- 2
252 is composite. Its prime factorisation is
- 3
The divisors add up to 728; without 252 itself that is 476, so 252 is abundant (476 is more than 252). Euler's totient φ(252) = 72 numbers up to 252 share no factor with it.
- 4
The digits of 252 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 109 steps to reach 1.
LaTeX source of the formulas on this page
\[ 252 = 2^{2} \times 3^{2} \times 7 \]252 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 728 |
| Euler totient φ(n) | 72 |
| Square | 63504 |
| Cube | 16003008 |
| Square root | 15.874508 (= 6√7) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 109 |
| Scientific notation | 2.52 × |
252 in other forms
| Form | Value |
|---|---|
| In words | two hundred and fifty-two |
| Roman numerals | CCLII |
| Binary (base 2) | 11111100 |
| Octal (base 8) | 374 |
| Hexadecimal (base 16) | FC |
| Base 3 | 100100 |
| As time | 252 seconds = 4 min 12 s |
Is 252 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (252 ÷ 2 = 126) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (252 ÷ 3 = 84) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (252 ÷ 4 = 63) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (252 ÷ 6 = 42) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (252 ÷ 7 = 36) | 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 | Yes (252 ÷ 9 = 28) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 | Yes (252 ÷ 12 = 21) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 252 a prime number?
No. 252 = × × 7, so it is divisible by 2.
What are the factors of 252?
1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
What is 252 in binary?
11111100 (hexadecimal FC, octal 374).
What is the square root of 252?
About 15.8745, exactly 6√7.
What is 252 in Roman numerals?
CCLII.
Is 252 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 252?
252 is a palindrome: it reads 252 backwards too; a Harshad number: divisible by its digit sum 9.