The number 72100
72100 is a composite number with 36 divisors. Its prime factorisation is × × 7 × 103. Divisors (36): 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 103, 140 … 72100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72100: a Harshad number: divisible by its digit sum 10.
- 2
72100 is composite. Its prime factorisation is
- 3
The divisors add up to 180544; without 72100 itself that is 108444, so 72100 is abundant (108444 is more than 72100). Euler's totient φ(72100) = 24480 numbers up to 72100 share no factor with it.
- 4
The digits of 72100 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 68 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72100 = 2^{2} \times 5^{2} \times 7 \times 103 \]72100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 180544 |
| Euler totient φ(n) | 24480 |
| Square | 5198410000 |
| Cube | 374805361000000 |
| Square root | 268.514432 (= 10√721) |
| Digit sum / digital root | 10 / 1 |
| Collatz steps to 1 | 68 |
| Scientific notation | 7.21 × |
72100 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand one hundred |
| Binary (base 2) | 10001100110100100 |
| Octal (base 8) | 214644 |
| Hexadecimal (base 16) | 119A4 |
| Base 3 | 10122220101 |
| As time | 72100 seconds = 20 h 1 min 40 s |
Is 72100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72100 ÷ 2 = 36050) | 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 (72100 ÷ 4 = 18025) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (72100 ÷ 5 = 14420) | 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 | Yes (72100 ÷ 7 = 10300) | 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 (72100 ÷ 10 = 7210) | 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 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72100 a prime number?
No. 72100 = × × 7 × 103, so it is divisible by 2.
What are the factors of 72100?
1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 103, 140, 175, 206, 350, 412, 515, 700, 721, 1030, 1442, 2060, 2575, 2884, 3605, 5150, 7210, 10300, 14420, 18025, 36050, 72100.
What is 72100 in binary?
10001100110100100 (hexadecimal 119A4, octal 214644).
What is the square root of 72100?
About 268.5144, exactly 10√721.
Is 72100 divisible by 3?
No. Its digits add up to 10, which is not a multiple of 3.
What is special about the number 72100?
72100 is a Harshad number: divisible by its digit sum 10.