The number 67200
67200 is a composite number with 96 divisors. Its prime factorisation is × 3 × × 7. Divisors (96): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24 … 67200.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 67200: a Harshad number: divisible by its digit sum 15.
- 2
67200 is composite. Its prime factorisation is
- 3
The divisors add up to 252960; without 67200 itself that is 185760, so 67200 is abundant (185760 is more than 67200). Euler's totient φ(67200) = 15360 numbers up to 67200 share no factor with it.
- 4
The digits of 67200 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67200 = 2^{7} \times 3 \times 5^{2} \times 7 \]67200 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 96 |
| Sum of divisors | 252960 |
| Euler totient φ(n) | 15360 |
| Square | 4515840000 |
| Cube | 303464448000000 |
| Square root | 259.229628 (= 40√42) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 37 |
| Scientific notation | 6.72 × |
67200 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand two hundred |
| Binary (base 2) | 10000011010000000 |
| Octal (base 8) | 203200 |
| Hexadecimal (base 16) | 10680 |
| Base 3 | 10102011220 |
| As time | 67200 seconds = 18 h 40 min 0 s |
Is 67200 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67200 ÷ 2 = 33600) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67200 ÷ 3 = 22400) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67200 ÷ 4 = 16800) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (67200 ÷ 5 = 13440) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (67200 ÷ 6 = 11200) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (67200 ÷ 7 = 9600) | 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 (67200 ÷ 8 = 8400) | 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 (67200 ÷ 10 = 6720) | 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 | Yes (67200 ÷ 12 = 5600) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67200 a prime number?
No. 67200 = × 3 × × 7, so it is divisible by 2.
What are the factors of 67200?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 64, 70, 75, 80, 84, 96, 100, 105, 112, 120, 128, 140, 150, 160, 168, 175, 192, 200, 210, 224, 240, 280, 300, 320, 336, 350, 384, 400, 420, 448, 480, 525, 560, 600, 640, 672, 700, 800, 840, 896, 960, 1050, 1120, 1200, 1344, 1400, 1600, 1680, 1920, 2100, 2240, 2400, 2688, 2800, 3200, 3360, 4200, 4480, 4800, 5600, 6720, 8400, 9600, 11200, 13440, 16800, 22400, 33600, 67200.
What is 67200 in binary?
10000011010000000 (hexadecimal 10680, octal 203200).
What is the square root of 67200?
About 259.2296, exactly 40√42.
Is 67200 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 67200?
67200 is a Harshad number: divisible by its digit sum 15.