The number 74400
74400 is a composite number with 72 divisors. Its prime factorisation is × 3 × × 31. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 31 … 74400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 74400: a Harshad number: divisible by its digit sum 15.
- 2
74400 is composite. Its prime factorisation is
- 3
The divisors add up to 249984; without 74400 itself that is 175584, so 74400 is abundant (175584 is more than 74400). Euler's totient φ(74400) = 19200 numbers up to 74400 share no factor with it.
- 4
The digits of 74400 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 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 74400 = 2^{5} \times 3 \times 5^{2} \times 31 \]74400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 249984 |
| Euler totient φ(n) | 19200 |
| Square | 5535360000 |
| Cube | 411830784000000 |
| Square root | 272.763634 (= 20√186) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.44 × |
74400 in other forms
| Form | Value |
|---|---|
| In words | seventy-four thousand four hundred |
| Binary (base 2) | 10010001010100000 |
| Octal (base 8) | 221240 |
| Hexadecimal (base 16) | 122A0 |
| Base 3 | 10210001120 |
| As time | 74400 seconds = 20 h 40 min 0 s |
Is 74400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (74400 ÷ 2 = 37200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (74400 ÷ 3 = 24800) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (74400 ÷ 4 = 18600) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (74400 ÷ 5 = 14880) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (74400 ÷ 6 = 12400) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (74400 ÷ 8 = 9300) | 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 (74400 ÷ 10 = 7440) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (74400 ÷ 12 = 6200) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 74400 a prime number?
No. 74400 = × 3 × × 31, so it is divisible by 2.
What are the factors of 74400?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 31, 32, 40, 48, 50, 60, 62, 75, 80, 93, 96, 100, 120, 124, 150, 155, 160, 186, 200, 240, 248, 300, 310, 372, 400, 465, 480, 496, 600, 620, 744, 775, 800, 930, 992, 1200, 1240, 1488, 1550, 1860, 2325, 2400, 2480, 2976, 3100, 3720, 4650, 4960, 6200, 7440, 9300, 12400, 14880, 18600, 24800, 37200, 74400.
What is 74400 in binary?
10010001010100000 (hexadecimal 122A0, octal 221240).
What is the square root of 74400?
About 272.7636, exactly 20√186.
Is 74400 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 74400?
74400 is a Harshad number: divisible by its digit sum 15.