The number 90100
90100 is a triangular number: 1 + 2 + … + 424 = 90100. Its prime factorisation is × × 17 × 53. Divisors (36): 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 53, 68, 85, 100, 106, 170 … 90100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 90100: a triangular number: 1 + 2 + … + 424 = 90100; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.
- 2
90100 is composite. Its prime factorisation is
- 3
The divisors add up to 210924; without 90100 itself that is 120824, so 90100 is abundant (120824 is more than 90100). Euler's totient φ(90100) = 33280 numbers up to 90100 share no factor with it.
- 4
The digits of 90100 add up to 10, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 164 steps to reach 1.
LaTeX source of the formulas on this page
\[ 90100 = 2^{2} \times 5^{2} \times 17 \times 53 \]90100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 210924 |
| Euler totient φ(n) | 33280 |
| Square | 8118010000 |
| Cube | 731432701000000 |
| Square root | 300.166620 (= 10√901) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 164 |
| Scientific notation | 9.01 × |
90100 in other forms
| Form | Value |
|---|---|
| In words | ninety thousand one hundred |
| Binary (base 2) | 10101111111110100 |
| Octal (base 8) | 257764 |
| Hexadecimal (base 16) | 15FF4 |
| Base 3 | 11120121001 |
| As time | 90100 seconds = 25 h 1 min 40 s |
Is 90100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (90100 ÷ 2 = 45050) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (90100 ÷ 4 = 22525) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (90100 ÷ 5 = 18020) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | 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 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (90100 ÷ 10 = 9010) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 90100 a prime number?
No. 90100 = × × 17 × 53, so it is divisible by 2.
What are the factors of 90100?
1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 53, 68, 85, 100, 106, 170, 212, 265, 340, 425, 530, 850, 901, 1060, 1325, 1700, 1802, 2650, 3604, 4505, 5300, 9010, 18020, 22525, 45050, 90100.
What is 90100 in binary?
10101111111110100 (hexadecimal 15FF4, octal 257764).
What is the square root of 90100?
About 300.1666, exactly 10√901.
Is 90100 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 90100?
90100 is a triangular number: 1 + 2 + … + 424 = 90100; a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 10.