The number 62400
62400 is a composite number with 84 divisors. Its prime factorisation is × 3 × × 13. Divisors (84): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26 … 62400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 62400: a Harshad number: divisible by its digit sum 12.
- 2
62400 is composite. Its prime factorisation is
- 3
The divisors add up to 220472; without 62400 itself that is 158072, so 62400 is abundant (158072 is more than 62400). Euler's totient φ(62400) = 15360 numbers up to 62400 share no factor with it.
- 4
The digits of 62400 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 148 steps to reach 1.
LaTeX source of the formulas on this page
\[ 62400 = 2^{6} \times 3 \times 5^{2} \times 13 \]62400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 84 |
| Sum of divisors | 220472 |
| Euler totient φ(n) | 15360 |
| Square | 3893760000 |
| Cube | 242970624000000 |
| Square root | 249.799920 (= 40√39) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 148 |
| Scientific notation | 6.24 × |
62400 in other forms
| Form | Value |
|---|---|
| In words | sixty-two thousand four hundred |
| Binary (base 2) | 1111001111000000 |
| Octal (base 8) | 171700 |
| Hexadecimal (base 16) | F3C0 |
| Base 3 | 10011121010 |
| As time | 62400 seconds = 17 h 20 min 0 s |
Is 62400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (62400 ÷ 2 = 31200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (62400 ÷ 3 = 20800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (62400 ÷ 4 = 15600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (62400 ÷ 5 = 12480) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (62400 ÷ 6 = 10400) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (62400 ÷ 8 = 7800) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (62400 ÷ 10 = 6240) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (62400 ÷ 12 = 5200) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 62400 a prime number?
No. 62400 = × 3 × × 13, so it is divisible by 2.
What are the factors of 62400?
1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 64, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 192, 195, 200, 208, 240, 260, 300, 312, 320, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 832, 960, 975, 1040, 1200, 1248, 1300, 1560, 1600, 1950, 2080, 2400, 2496, 2600, 3120, 3900, 4160, 4800, 5200, 6240, 7800, 10400, 12480, 15600, 20800, 31200, 62400.
What is 62400 in binary?
1111001111000000 (hexadecimal F3C0, octal 171700).
What is the square root of 62400?
About 249.7999, exactly 40√39.
Is 62400 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 62400?
62400 is a Harshad number: divisible by its digit sum 12.