The number 20100
20100 is a triangular number: 1 + 2 + … + 200 = 20100. Its prime factorisation is × 3 × × 67. Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 67, 75 … 20100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20100: a triangular number: 1 + 2 + … + 200 = 20100; a Harshad number: divisible by its digit sum 3.
- 2
20100 is composite. Its prime factorisation is
- 3
The divisors add up to 59024; without 20100 itself that is 38924, so 20100 is abundant (38924 is more than 20100). Euler's totient φ(20100) = 5280 numbers up to 20100 share no factor with it.
- 4
The digits of 20100 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 118 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20100 = 2^{2} \times 3 \times 5^{2} \times 67 \]20100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 59024 |
| Euler totient φ(n) | 5280 |
| Square | 404010000 |
| Cube | 8120601000000 |
| Square root | 141.774469 (= 10√201) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 118 |
| Scientific notation | 2.01 × |
20100 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand one hundred |
| Binary (base 2) | 100111010000100 |
| Octal (base 8) | 47204 |
| Hexadecimal (base 16) | 4E84 |
| Base 3 | 1000120110 |
| As time | 20100 seconds = 5 h 35 min 0 s |
Is 20100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20100 ÷ 2 = 10050) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (20100 ÷ 3 = 6700) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (20100 ÷ 4 = 5025) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (20100 ÷ 5 = 4020) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (20100 ÷ 6 = 3350) | 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 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (20100 ÷ 10 = 2010) | 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 | Yes (20100 ÷ 12 = 1675) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20100 a prime number?
No. 20100 = × 3 × × 67, so it is divisible by 2.
What are the factors of 20100?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 67, 75, 100, 134, 150, 201, 268, 300, 335, 402, 670, 804, 1005, 1340, 1675, 2010, 3350, 4020, 5025, 6700, 10050, 20100.
What is 20100 in binary?
100111010000100 (hexadecimal 4E84, octal 47204).
What is the square root of 20100?
About 141.7745, exactly 10√201.
Is 20100 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 20100?
20100 is a triangular number: 1 + 2 + … + 200 = 20100; a Harshad number: divisible by its digit sum 3.