The number 87872
87872 is a composite number with 14 divisors. Its prime factorisation is × 1373. Divisors (14): 1, 2, 4, 8, 16, 32, 64, 1373, 2746, 5492, 10984, 21968, 43936, 87872.
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How to work it out
- 1
What is special about 87872: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 32.
- 2
87872 is composite. Its prime factorisation is
- 3
The divisors add up to 174498; without 87872 itself that is 86626, so 87872 is deficient (86626 is less than 87872). Euler's totient φ(87872) = 43904 numbers up to 87872 share no factor with it.
- 4
The digits of 87872 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 133 steps to reach 1.
LaTeX source of the formulas on this page
\[ 87872 = 2^{6} \times 1373 \]87872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 14 |
| Sum of divisors | 174498 |
| Euler totient φ(n) | 43904 |
| Square | 7721488384 |
| Cube | 678502627278848 |
| Square root | 296.432117 (= 8√1373) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 133 |
| Scientific notation | 8.7872 × |
87872 in other forms
| Form | Value |
|---|---|
| In words | eighty-seven thousand eight hundred and seventy-two |
| Binary (base 2) | 10101011101000000 |
| Octal (base 8) | 253500 |
| Hexadecimal (base 16) | 15740 |
| Base 3 | 11110112112 |
| As time | 87872 seconds = 24 h 24 min 32 s |
Is 87872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (87872 ÷ 2 = 43936) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (87872 ÷ 4 = 21968) | 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 | No (remainder 2) | 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 | Yes (87872 ÷ 8 = 10984) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 87872 a prime number?
No. 87872 = × 1373, so it is divisible by 2.
What are the factors of 87872?
1, 2, 4, 8, 16, 32, 64, 1373, 2746, 5492, 10984, 21968, 43936, 87872.
What is 87872 in binary?
10101011101000000 (hexadecimal 15740, octal 253500).
What is the square root of 87872?
About 296.4321, exactly 8√1373.
Is 87872 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 87872?
87872 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 32.