The number 31200
31200 is a composite number with 72 divisors. Its prime factorisation is × 3 × × 13. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26 … 31200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 31200: a Harshad number: divisible by its digit sum 6.
- 2
31200 is composite. Its prime factorisation is
- 3
The divisors add up to 109368; without 31200 itself that is 78168, so 31200 is abundant (78168 is more than 31200). Euler's totient φ(31200) = 7680 numbers up to 31200 share no factor with it.
- 4
The digits of 31200 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 147 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31200 = 2^{5} \times 3 \times 5^{2} \times 13 \]31200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 109368 |
| Euler totient φ(n) | 7680 |
| Square | 973440000 |
| Cube | 30371328000000 |
| Square root | 176.635217 (= 20√78) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 147 |
| Scientific notation | 3.12 × |
31200 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand two hundred |
| Binary (base 2) | 111100111100000 |
| Octal (base 8) | 74740 |
| Hexadecimal (base 16) | 79E0 |
| Base 3 | 1120210120 |
| As time | 31200 seconds = 8 h 40 min 0 s |
Is 31200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31200 ÷ 2 = 15600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31200 ÷ 3 = 10400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (31200 ÷ 4 = 7800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31200 ÷ 5 = 6240) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31200 ÷ 6 = 5200) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 | Yes (31200 ÷ 8 = 3900) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31200 ÷ 10 = 3120) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (31200 ÷ 12 = 2600) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31200 a prime number?
No. 31200 = × 3 × × 13, so it is divisible by 2.
What are the factors of 31200?
1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 195, 200, 208, 240, 260, 300, 312, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 975, 1040, 1200, 1248, 1300, 1560, 1950, 2080, 2400, 2600, 3120, 3900, 5200, 6240, 7800, 10400, 15600, 31200.
What is 31200 in binary?
111100111100000 (hexadecimal 79E0, octal 74740).
What is the square root of 31200?
About 176.6352, exactly 20√78.
Is 31200 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 31200?
31200 is a Harshad number: divisible by its digit sum 6.