The number 87972
87972 is a composite number with 12 divisors. Its prime factorisation is × 3 × 7331. Divisors (12): 1, 2, 3, 4, 6, 12, 7331, 14662, 21993, 29324, 43986, 87972.
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How to work it out
- 1
87972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
87972 is composite. Its prime factorisation is
- 3
The divisors add up to 205296; without 87972 itself that is 117324, so 87972 is abundant (117324 is more than 87972). Euler's totient φ(87972) = 29320 numbers up to 87972 share no factor with it.
- 4
The digits of 87972 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 151 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87972 = 2^{2} \times 3 \times 7331 \]87972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 205296 |
| Euler totient φ(n) | 29320 |
| Square | 7739072784 |
| Cube | 680821710954048 |
| Square root | 296.600742 (= 2√21993) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 151 |
| Scientific notation | 8.7972 × |
87972 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand nine hundred and seventy-two |
| Binary (base 2) | 10101011110100100 |
| Octal (base 8) | 253644 |
| Hexadecimal (base 16) | 157A4 |
| Base 3 | 11110200020 |
| As time | 87972 seconds = 24 h 26 min 12 s |
Is 87972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87972 ÷ 2 = 43986) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (87972 ÷ 3 = 29324) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87972 ÷ 4 = 21993) | 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 (87972 ÷ 6 = 14662) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 6) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (87972 ÷ 12 = 7331) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87972 a prime number?
No. 87972 = × 3 × 7331, so it is divisible by 2.
What are the factors of 87972?
1, 2, 3, 4, 6, 12, 7331, 14662, 21993, 29324, 43986, 87972.
What is 87972 in binary?
10101011110100100 (hexadecimal 157A4, octal 253644).
What is the square root of 87972?
About 296.6007, exactly 2√21993.
Is 87972 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 87972?
It is a composite number with 12 divisors.