The number 39480
39480 is a composite number with 64 divisors. Its prime factorisation is × 3 × 5 × 7 × 47. Divisors (64): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28 … 39480.
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How to work it out
- 1
What is special about 39480: a Harshad number: divisible by its digit sum 24.
- 2
39480 is composite. Its prime factorisation is
- 3
The divisors add up to 138240; without 39480 itself that is 98760, so 39480 is abundant (98760 is more than 39480). Euler's totient φ(39480) = 8832 numbers up to 39480 share no factor with it.
- 4
The digits of 39480 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 199 steps to reach 1.
LaTeX source of the formulas on this page
\[ 39480 = 2^{3} \times 3 \times 5 \times 7 \times 47 \]39480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 138240 |
| Euler totient φ(n) | 8832 |
| Square | 1558670400 |
| Cube | 61536307392000 |
| Square root | 198.695747 (= 2√9870) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 199 |
| Scientific notation | 3.948 × |
39480 in other forms
| Form | Value |
|---|---|
| In words | thirty-nine thousand four hundred and eighty |
| Binary (base 2) | 1001101000111000 |
| Octal (base 8) | 115070 |
| Hexadecimal (base 16) | 9A38 |
| Base 3 | 2000011020 |
| As time | 39480 seconds = 10 h 58 min 0 s |
Is 39480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (39480 ÷ 2 = 19740) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (39480 ÷ 3 = 13160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (39480 ÷ 4 = 9870) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (39480 ÷ 5 = 7896) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (39480 ÷ 6 = 6580) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (39480 ÷ 7 = 5640) | 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 | Yes (39480 ÷ 8 = 4935) | 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 (39480 ÷ 10 = 3948) | 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 (39480 ÷ 12 = 3290) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 39480 a prime number?
No. 39480 = × 3 × 5 × 7 × 47, so it is divisible by 2.
What are the factors of 39480?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 47, 56, 60, 70, 84, 94, 105, 120, 140, 141, 168, 188, 210, 235, 280, 282, 329, 376, 420, 470, 564, 658, 705, 840, 940, 987, 1128, 1316, 1410, 1645, 1880, 1974, 2632, 2820, 3290, 3948, 4935, 5640, 6580, 7896, 9870, 13160, 19740, 39480.
What is 39480 in binary?
1001101000111000 (hexadecimal 9A38, octal 115070).
What is the square root of 39480?
About 198.6957, exactly 2√9870.
Is 39480 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 39480?
39480 is a Harshad number: divisible by its digit sum 24.