The number 4140
4140 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 23. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 30, 36, 45 … 4140.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 4140: a Harshad number: divisible by its digit sum 9.
- 2
4140 is composite. Its prime factorisation is
- 3
The divisors add up to 13104; without 4140 itself that is 8964, so 4140 is abundant (8964 is more than 4140). Euler's totient φ(4140) = 1056 numbers up to 4140 share no factor with it.
- 4
The digits of 4140 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 126 steps to reach 1.
LaTeX source of the formulas on this page
\[ 4140 = 2^{2} \times 3^{2} \times 5 \times 23 \]4140 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 13104 |
| Euler totient φ(n) | 1056 |
| Square | 17139600 |
| Cube | 70957944000 |
| Square root | 64.342832 (= 6√115) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 126 |
| Scientific notation | 4.14 × |
4140 in other forms
| Form | Value |
|---|---|
| In words | four thousand one hundred and forty |
| Binary (base 2) | 1000000101100 |
| Octal (base 8) | 10054 |
| Hexadecimal (base 16) | 102C |
| Base 3 | 12200100 |
| As time | 4140 seconds = 1 h 9 min 0 s |
Is 4140 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (4140 ÷ 2 = 2070) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (4140 ÷ 3 = 1380) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (4140 ÷ 4 = 1035) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (4140 ÷ 5 = 828) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (4140 ÷ 6 = 690) | 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 | Yes (4140 ÷ 9 = 460) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (4140 ÷ 10 = 414) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (4140 ÷ 12 = 345) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 4140 a prime number?
No. 4140 = × × 5 × 23, so it is divisible by 2.
What are the factors of 4140?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 30, 36, 45, 46, 60, 69, 90, 92, 115, 138, 180, 207, 230, 276, 345, 414, 460, 690, 828, 1035, 1380, 2070, 4140.
What is 4140 in binary?
1000000101100 (hexadecimal 102C, octal 10054).
What is the square root of 4140?
About 64.3428, exactly 6√115.
Is 4140 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 4140?
4140 is a Harshad number: divisible by its digit sum 9.