The number 7140
7140 is a triangular number: 1 + 2 + … + 119 = 7140. Its prime factorisation is × 3 × 5 × 7 × 17. Divisors (48): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30 … 7140.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 7140: a triangular number: 1 + 2 + … + 119 = 7140; a Harshad number: divisible by its digit sum 12.
- 2
7140 is composite. Its prime factorisation is
- 3
The divisors add up to 24192; without 7140 itself that is 17052, so 7140 is abundant (17052 is more than 7140). Euler's totient φ(7140) = 1536 numbers up to 7140 share no factor with it.
- 4
The digits of 7140 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 31 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7140 = 2^{2} \times 3 \times 5 \times 7 \times 17 \]7140 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 24192 |
| Euler totient φ(n) | 1536 |
| Square | 50979600 |
| Cube | 363994344000 |
| Square root | 84.498521 (= 2√1785) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 31 |
| Scientific notation | 7.14 × |
7140 in other forms
| Form | Value |
|---|---|
| In words | seven thousand one hundred and forty |
| Binary (base 2) | 1101111100100 |
| Octal (base 8) | 15744 |
| Hexadecimal (base 16) | 1BE4 |
| Base 3 | 100210110 |
| As time | 7140 seconds = 1 h 59 min 0 s |
Is 7140 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7140 ÷ 2 = 3570) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7140 ÷ 3 = 2380) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (7140 ÷ 4 = 1785) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (7140 ÷ 5 = 1428) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (7140 ÷ 6 = 1190) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (7140 ÷ 7 = 1020) | 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 (7140 ÷ 10 = 714) | 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 | Yes (7140 ÷ 12 = 595) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 7140 a prime number?
No. 7140 = × 3 × 5 × 7 × 17, so it is divisible by 2.
What are the factors of 7140?
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140.
What is 7140 in binary?
1101111100100 (hexadecimal 1BE4, octal 15744).
What is the square root of 7140?
About 84.4985, exactly 2√1785.
Is 7140 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 7140?
7140 is a triangular number: 1 + 2 + … + 119 = 7140; a Harshad number: divisible by its digit sum 12.