The number 98400
98400 is a composite number with 72 divisors. Its prime factorisation is × 3 × × 41. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32 … 98400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
98400 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
98400 is composite. Its prime factorisation is
- 3
The divisors add up to 328104; without 98400 itself that is 229704, so 98400 is abundant (229704 is more than 98400). Euler's totient φ(98400) = 25600 numbers up to 98400 share no factor with it.
- 4
The digits of 98400 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 159 steps to reach 1.
LaTeX source of the formulas on this page
\[ 98400 = 2^{5} \times 3 \times 5^{2} \times 41 \]98400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 328104 |
| Euler totient φ(n) | 25600 |
| Square | 9682560000 |
| Cube | 952763904000000 |
| Square root | 313.687743 (= 20√246) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 159 |
| Scientific notation | 9.84 × |
98400 in other forms
| Form | Value |
|---|---|
| In words | ninety-eight thousand four hundred |
| Binary (base 2) | 11000000001100000 |
| Octal (base 8) | 300140 |
| Hexadecimal (base 16) | 18060 |
| Base 3 | 11222222110 |
| As time | 98400 seconds = 27 h 20 min 0 s |
Is 98400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (98400 ÷ 2 = 49200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (98400 ÷ 3 = 32800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (98400 ÷ 4 = 24600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (98400 ÷ 5 = 19680) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (98400 ÷ 6 = 16400) | 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 (98400 ÷ 8 = 12300) | 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 (98400 ÷ 10 = 9840) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (98400 ÷ 12 = 8200) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 98400 a prime number?
No. 98400 = × 3 × × 41, so it is divisible by 2.
What are the factors of 98400?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 41, 48, 50, 60, 75, 80, 82, 96, 100, 120, 123, 150, 160, 164, 200, 205, 240, 246, 300, 328, 400, 410, 480, 492, 600, 615, 656, 800, 820, 984, 1025, 1200, 1230, 1312, 1640, 1968, 2050, 2400, 2460, 3075, 3280, 3936, 4100, 4920, 6150, 6560, 8200, 9840, 12300, 16400, 19680, 24600, 32800, 49200, 98400.
What is 98400 in binary?
11000000001100000 (hexadecimal 18060, octal 300140).
What is the square root of 98400?
About 313.6877, exactly 20√246.
Is 98400 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 98400?
It is a composite number with 72 divisors.