The number 31950
31950 is a composite number with 36 divisors. Its prime factorisation is 2 × × × 71. Divisors (36): 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 71, 75, 90 … 31950.
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How to work it out
- 1
What is special about 31950: a Harshad number: divisible by its digit sum 18.
- 2
31950 is composite. Its prime factorisation is
- 3
The divisors add up to 87048; without 31950 itself that is 55098, so 31950 is abundant (55098 is more than 31950). Euler's totient φ(31950) = 8400 numbers up to 31950 share no factor with it.
- 4
The digits of 31950 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 98 steps to reach 1.
LaTeX source of the formulas on this page
\[ 31950 = 2 \times 3^{2} \times 5^{2} \times 71 \]31950 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 87048 |
| Euler totient φ(n) | 8400 |
| Square | 1020802500 |
| Cube | 32614639875000 |
| Square root | 178.745629 (= 15√142) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 98 |
| Scientific notation | 3.195 × |
31950 in other forms
| Form | Value |
|---|---|
| In words | thirty-one thousand nine hundred and fifty |
| Binary (base 2) | 111110011001110 |
| Octal (base 8) | 76316 |
| Hexadecimal (base 16) | 7CCE |
| Base 3 | 1121211100 |
| As time | 31950 seconds = 8 h 52 min 30 s |
Is 31950 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (31950 ÷ 2 = 15975) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (31950 ÷ 3 = 10650) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (31950 ÷ 5 = 6390) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (31950 ÷ 6 = 5325) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (31950 ÷ 9 = 3550) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (31950 ÷ 10 = 3195) | 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 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 31950 a prime number?
No. 31950 = 2 × × × 71, so it is divisible by 2.
What are the factors of 31950?
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 71, 75, 90, 142, 150, 213, 225, 355, 426, 450, 639, 710, 1065, 1278, 1775, 2130, 3195, 3550, 5325, 6390, 10650, 15975, 31950.
What is 31950 in binary?
111110011001110 (hexadecimal 7CCE, octal 76316).
What is the square root of 31950?
About 178.7456, exactly 15√142.
Is 31950 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 31950?
31950 is a Harshad number: divisible by its digit sum 18.