The number 25200
25200 is a highly composite number: it has 90 divisors, more than any smaller number and a triangular number: 1 + 2 + … + 224 = 25200. Its prime factorisation is × × × 7. Divisors (90): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20 … 25200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 25200: a highly composite number: it has 90 divisors, more than any smaller number; a triangular number: 1 + 2 + … + 224 = 25200; a Harshad number: divisible by its digit sum 9.
- 2
25200 is composite. Its prime factorisation is
- 3
The divisors add up to 99944; without 25200 itself that is 74744, so 25200 is abundant (74744 is more than 25200). Euler's totient φ(25200) = 5760 numbers up to 25200 share no factor with it.
- 4
The digits of 25200 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 64 steps to reach 1.
LaTeX source of the formulas on this page
\[ 25200 = 2^{4} \times 3^{2} \times 5^{2} \times 7 \]25200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 90 |
| Sum of divisors | 99944 |
| Euler totient φ(n) | 5760 |
| Square | 635040000 |
| Cube | 16003008000000 |
| Square root | 158.745079 (= 60√7) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 64 |
| Scientific notation | 2.52 × |
25200 in other forms
| Form | Value |
|---|---|
| In words | twenty-five thousand two hundred |
| Binary (base 2) | 110001001110000 |
| Octal (base 8) | 61160 |
| Hexadecimal (base 16) | 6270 |
| Base 3 | 1021120100 |
| As time | 25200 seconds = 7 h 0 min 0 s |
Is 25200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (25200 ÷ 2 = 12600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (25200 ÷ 3 = 8400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (25200 ÷ 4 = 6300) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (25200 ÷ 5 = 5040) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (25200 ÷ 6 = 4200) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (25200 ÷ 7 = 3600) | 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 (25200 ÷ 8 = 3150) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (25200 ÷ 9 = 2800) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (25200 ÷ 10 = 2520) | 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 (25200 ÷ 12 = 2100) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 25200 a prime number?
No. 25200 = × × × 7, so it is divisible by 2.
What are the factors of 25200?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 48, 50, 56, 60, 63, 70, 72, 75, 80, 84, 90, 100, 105, 112, 120, 126, 140, 144, 150, 168, 175, 180, 200, 210, 225, 240, 252, 280, 300, 315, 336, 350, 360, 400, 420, 450, 504, 525, 560, 600, 630, 700, 720, 840, 900, 1008, 1050, 1200, 1260, 1400, 1575, 1680, 1800, 2100, 2520, 2800, 3150, 3600, 4200, 5040, 6300, 8400, 12600, 25200.
What is 25200 in binary?
110001001110000 (hexadecimal 6270, octal 61160).
What is the square root of 25200?
About 158.7451, exactly 60√7.
Is 25200 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 25200?
25200 is a highly composite number: it has 90 divisors, more than any smaller number; a triangular number: 1 + 2 + … + 224 = 25200; a Harshad number: divisible by its digit sum 9.