The number 83970
83970 is a composite number with 32 divisors. Its prime factorisation is 2 × × 5 × 311. Divisors (32): 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270 … 83970.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 83970: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
83970 is composite. Its prime factorisation is
- 3
The divisors add up to 224640; without 83970 itself that is 140670, so 83970 is abundant (140670 is more than 83970). Euler's totient φ(83970) = 22320 numbers up to 83970 share no factor with it.
- 4
The digits of 83970 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 120 steps to reach 1.
LaTeX source of the formulas on this page
\[ 83970 = 2 \times 3^{3} \times 5 \times 311 \]83970 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 224640 |
| Euler totient φ(n) | 22320 |
| Square | 7050960900 |
| Cube | 592069186773000 |
| Square root | 289.775775 (= 3√9330) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 120 |
| Scientific notation | 8.397 × |
83970 in other forms
| Form | Value |
|---|---|
| In words | eighty-three thousand nine hundred and seventy |
| Binary (base 2) | 10100100000000010 |
| Octal (base 8) | 244002 |
| Hexadecimal (base 16) | 14802 |
| Base 3 | 11021012000 |
| As time | 83970 seconds = 23 h 19 min 30 s |
Is 83970 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (83970 ÷ 2 = 41985) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (83970 ÷ 3 = 27990) | 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 (83970 ÷ 5 = 16794) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (83970 ÷ 6 = 13995) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 2) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (83970 ÷ 9 = 9330) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (83970 ÷ 10 = 8397) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | 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 83970 a prime number?
No. 83970 = 2 × × 5 × 311, so it is divisible by 2.
What are the factors of 83970?
1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270, 311, 622, 933, 1555, 1866, 2799, 3110, 4665, 5598, 8397, 9330, 13995, 16794, 27990, 41985, 83970.
What is 83970 in binary?
10100100000000010 (hexadecimal 14802, octal 244002).
What is the square root of 83970?
About 289.7758, exactly 3√9330.
Is 83970 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 83970?
83970 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.