The number 72408
72408 is a composite number with 32 divisors. Its prime factorisation is × 3 × 7 × 431. Divisors (32): 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168 … 72408.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72408: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.
- 2
72408 is composite. Its prime factorisation is
- 3
The divisors add up to 207360; without 72408 itself that is 134952, so 72408 is abundant (134952 is more than 72408). Euler's totient φ(72408) = 20640 numbers up to 72408 share no factor with it.
- 4
The digits of 72408 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 94 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72408 = 2^{3} \times 3 \times 7 \times 431 \]72408 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 207360 |
| Euler totient φ(n) | 20640 |
| Square | 5242918464 |
| Cube | 379629240141312 |
| Square root | 269.087346 (= 2√18102) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 94 |
| Scientific notation | 7.2408 × |
72408 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand four hundred and eight |
| Binary (base 2) | 10001101011011000 |
| Octal (base 8) | 215330 |
| Hexadecimal (base 16) | 11AD8 |
| Base 3 | 10200022210 |
| As time | 72408 seconds = 20 h 6 min 48 s |
Is 72408 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72408 ÷ 2 = 36204) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72408 ÷ 3 = 24136) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72408 ÷ 4 = 18102) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72408 ÷ 6 = 12068) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (72408 ÷ 7 = 10344) | 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 (72408 ÷ 8 = 9051) | 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 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72408 ÷ 12 = 6034) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72408 a prime number?
No. 72408 = × 3 × 7 × 431, so it is divisible by 2.
What are the factors of 72408?
1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168, 431, 862, 1293, 1724, 2586, 3017, 3448, 5172, 6034, 9051, 10344, 12068, 18102, 24136, 36204, 72408.
What is 72408 in binary?
10001101011011000 (hexadecimal 11AD8, octal 215330).
What is the square root of 72408?
About 269.0873, exactly 2√18102.
Is 72408 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 72408?
72408 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 21.