The number 75972
75972 is a composite number with 24 divisors. Its prime factorisation is × 3 × 13 × 487. Divisors (24): 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 487, 974, 1461, 1948 … 75972.
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How to work it out
- 1
What is special about 75972: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
75972 is composite. Its prime factorisation is
- 3
The divisors add up to 191296; without 75972 itself that is 115324, so 75972 is abundant (115324 is more than 75972). Euler's totient φ(75972) = 23328 numbers up to 75972 share no factor with it.
- 4
The digits of 75972 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 55 steps to reach 1.
LaTeX source of the formulas on this page
\[ 75972 = 2^{2} \times 3 \times 13 \times 487 \]75972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 191296 |
| Euler totient φ(n) | 23328 |
| Square | 5771744784 |
| Cube | 438490994730048 |
| Square root | 275.630187 (= 2√18993) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 55 |
| Scientific notation | 7.5972 × |
75972 in other forms
| Form | Value |
|---|---|
| In words | seventy-five thousand nine hundred and seventy-two |
| Binary (base 2) | 10010100011000100 |
| Octal (base 8) | 224304 |
| Hexadecimal (base 16) | 128C4 |
| Base 3 | 10212012210 |
| As time | 75972 seconds = 21 h 6 min 12 s |
Is 75972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (75972 ÷ 2 = 37986) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (75972 ÷ 3 = 25324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (75972 ÷ 4 = 18993) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (75972 ÷ 6 = 12662) | 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 | No (remainder 4) | 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 2) | 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 (75972 ÷ 12 = 6331) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 75972 a prime number?
No. 75972 = × 3 × 13 × 487, so it is divisible by 2.
What are the factors of 75972?
1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 487, 974, 1461, 1948, 2922, 5844, 6331, 12662, 18993, 25324, 37986, 75972.
What is 75972 in binary?
10010100011000100 (hexadecimal 128C4, octal 224304).
What is the square root of 75972?
About 275.6302, exactly 2√18993.
Is 75972 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 75972?
75972 is a happy number: repeatedly adding the squares of its digits reaches 1.