The number 10140
10140 is a composite number with 36 divisors. Its prime factorisation is × 3 × 5 × . Divisors (36): 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60 … 10140.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10140: a Harshad number: divisible by its digit sum 6.
- 2
10140 is composite. Its prime factorisation is
- 3
The divisors add up to 30744; without 10140 itself that is 20604, so 10140 is abundant (20604 is more than 10140). Euler's totient φ(10140) = 2496 numbers up to 10140 share no factor with it.
- 4
The digits of 10140 add up to 6, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 86 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10140 = 2^{2} \times 3 \times 5 \times 13^{2} \]10140 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 30744 |
| Euler totient φ(n) | 2496 |
| Square | 102819600 |
| Cube | 1042590744000 |
| Square root | 100.697567 (= 26√15) |
| Digit sum / digital root | 6 / 6 |
| Collatz steps to 1 | 86 |
| Scientific notation | 1.014 × |
10140 in other forms
| Form | Value |
|---|---|
| In words | ten thousand one hundred and forty |
| Binary (base 2) | 10011110011100 |
| Octal (base 8) | 23634 |
| Hexadecimal (base 16) | 279C |
| Base 3 | 111220120 |
| As time | 10140 seconds = 2 h 49 min 0 s |
Is 10140 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10140 ÷ 2 = 5070) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10140 ÷ 3 = 3380) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10140 ÷ 4 = 2535) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (10140 ÷ 5 = 2028) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (10140 ÷ 6 = 1690) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (10140 ÷ 10 = 1014) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10140 ÷ 12 = 845) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10140 a prime number?
No. 10140 = × 3 × 5 × , so it is divisible by 2.
What are the factors of 10140?
1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 169, 195, 260, 338, 390, 507, 676, 780, 845, 1014, 1690, 2028, 2535, 3380, 5070, 10140.
What is 10140 in binary?
10011110011100 (hexadecimal 279C, octal 23634).
What is the square root of 10140?
About 100.6976, exactly 26√15.
Is 10140 divisible by 3?
Yes. Its digits add up to 6, a multiple of 3.
What is special about the number 10140?
10140 is a Harshad number: divisible by its digit sum 6.