The number 872
872 is a composite number with 8 divisors. Its prime factorisation is × 109. Divisors (8): 1, 2, 4, 8, 109, 218, 436, 872.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
872 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
872 is composite. Its prime factorisation is
- 3
The divisors add up to 1650; without 872 itself that is 778, so 872 is deficient (778 is less than 872). Euler's totient φ(872) = 432 numbers up to 872 share no factor with it.
- 4
The digits of 872 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 116 steps to reach 1.
LaTeX source of the formulas on this page
\[ 872 = 2^{3} \times 109 \]872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1650 |
| Euler totient φ(n) | 432 |
| Square | 760384 |
| Cube | 663054848 |
| Square root | 29.529646 (= 2√218) |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 116 |
| Scientific notation | 8.72 × |
872 in other forms
| Form | Value |
|---|---|
| In words | eight hundred and seventy-two |
| Roman numerals | DCCCLXXII |
| Binary (base 2) | 1101101000 |
| Octal (base 8) | 1550 |
| Hexadecimal (base 16) | 368 |
| Base 3 | 1012022 |
| As time | 872 seconds = 14 min 32 s |
Is 872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (872 ÷ 2 = 436) | 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 (872 ÷ 4 = 218) | 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 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 (872 ÷ 8 = 109) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 3) | 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 872 a prime number?
No. 872 = × 109, so it is divisible by 2.
What are the factors of 872?
1, 2, 4, 8, 109, 218, 436, 872.
What is 872 in binary?
1101101000 (hexadecimal 368, octal 1550).
What is the square root of 872?
About 29.5296, exactly 2√218.
What is 872 in Roman numerals?
DCCCLXXII.
Is 872 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 872?
It is a composite number with 8 divisors.