The number 75420
75420 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 419. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 … 75420.
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How to work it out
- 1
What is special about 75420: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
75420 is composite. Its prime factorisation is
- 3
The divisors add up to 229320; without 75420 itself that is 153900, so 75420 is abundant (153900 is more than 75420). Euler's totient φ(75420) = 20064 numbers up to 75420 share no factor with it.
- 4
The digits of 75420 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 75420 = 2^{2} \times 3^{2} \times 5 \times 419 \]75420 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 229320 |
| Euler totient φ(n) | 20064 |
| Square | 5688176400 |
| Cube | 429002264088000 |
| Square root | 274.627020 (= 6√2095) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 107 |
| Scientific notation | 7.542 × |
75420 in other forms
| Form | Value |
|---|---|
| In words | seventy-five thousand four hundred and twenty |
| Binary (base 2) | 10010011010011100 |
| Octal (base 8) | 223234 |
| Hexadecimal (base 16) | 1269C |
| Base 3 | 10211110100 |
| As time | 75420 seconds = 20 h 57 min 0 s |
Is 75420 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (75420 ÷ 2 = 37710) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (75420 ÷ 3 = 25140) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (75420 ÷ 4 = 18855) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (75420 ÷ 5 = 15084) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (75420 ÷ 6 = 12570) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (75420 ÷ 9 = 8380) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (75420 ÷ 10 = 7542) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (75420 ÷ 12 = 6285) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 75420 a prime number?
No. 75420 = × × 5 × 419, so it is divisible by 2.
What are the factors of 75420?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 419, 838, 1257, 1676, 2095, 2514, 3771, 4190, 5028, 6285, 7542, 8380, 12570, 15084, 18855, 25140, 37710, 75420.
What is 75420 in binary?
10010011010011100 (hexadecimal 1269C, octal 223234).
What is the square root of 75420?
About 274.6270, exactly 6√2095.
Is 75420 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 75420?
75420 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.