The number 5050
5050 is a triangular number: 1 + 2 + … + 100 = 5050. Its prime factorisation is 2 × × 101. Divisors (12): 1, 2, 5, 10, 25, 50, 101, 202, 505, 1010, 2525, 5050.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 5050: a triangular number: 1 + 2 + … + 100 = 5050; a Harshad number: divisible by its digit sum 10.
- 2
5050 is composite. Its prime factorisation is
- 3
The divisors add up to 9486; without 5050 itself that is 4436, so 5050 is deficient (4436 is less than 5050). Euler's totient φ(5050) = 2000 numbers up to 5050 share no factor with it.
- 4
The digits of 5050 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 41 steps to reach 1.
LaTeX source of the formulas on this page
\[ 5050 = 2 \times 5^{2} \times 101 \]5050 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 9486 |
| Euler totient φ(n) | 2000 |
| Square | 25502500 |
| Cube | 128787625000 |
| Square root | 71.063352 (= 5√202) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 41 |
| Scientific notation | 5.05 × |
5050 in other forms
| Form | Value |
|---|---|
| In words | five thousand and fifty |
| Binary (base 2) | 1001110111010 |
| Octal (base 8) | 11672 |
| Hexadecimal (base 16) | 13BA |
| Base 3 | 20221001 |
| As time | 5050 seconds = 1 h 24 min 10 s |
Is 5050 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (5050 ÷ 2 = 2525) | 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 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (5050 ÷ 5 = 1010) | 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 2) | 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 (5050 ÷ 10 = 505) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 10) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 5050 a prime number?
No. 5050 = 2 × × 101, so it is divisible by 2.
What are the factors of 5050?
1, 2, 5, 10, 25, 50, 101, 202, 505, 1010, 2525, 5050.
What is 5050 in binary?
1001110111010 (hexadecimal 13BA, octal 11672).
What is the square root of 5050?
About 71.0634, exactly 5√202.
Is 5050 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 5050?
5050 is a triangular number: 1 + 2 + … + 100 = 5050; a Harshad number: divisible by its digit sum 10.