The number 42720
42720 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 89. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 42720.
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How to work it out
- 1
What is special about 42720: a Harshad number: divisible by its digit sum 15.
- 2
42720 is composite. Its prime factorisation is
- 3
The divisors add up to 136080; without 42720 itself that is 93360, so 42720 is abundant (93360 is more than 42720). Euler's totient φ(42720) = 11264 numbers up to 42720 share no factor with it.
- 4
The digits of 42720 add up to 15, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 150 steps to reach 1.
LaTeX source of the formulas on this page
\[ 42720 = 2^{5} \times 3 \times 5 \times 89 \]42720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 136080 |
| Euler totient φ(n) | 11264 |
| Square | 1824998400 |
| Cube | 77963931648000 |
| Square root | 206.688171 (= 4√2670) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 150 |
| Scientific notation | 4.272 × |
42720 in other forms
| Form | Value |
|---|---|
| In words | forty-two thousand seven hundred and twenty |
| Binary (base 2) | 1010011011100000 |
| Octal (base 8) | 123340 |
| Hexadecimal (base 16) | A6E0 |
| Base 3 | 2011121020 |
| As time | 42720 seconds = 11 h 52 min 0 s |
Is 42720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (42720 ÷ 2 = 21360) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (42720 ÷ 3 = 14240) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (42720 ÷ 4 = 10680) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (42720 ÷ 5 = 8544) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (42720 ÷ 6 = 7120) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (42720 ÷ 8 = 5340) | 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 (42720 ÷ 10 = 4272) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (42720 ÷ 12 = 3560) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 42720 a prime number?
No. 42720 = × 3 × 5 × 89, so it is divisible by 2.
What are the factors of 42720?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 89, 96, 120, 160, 178, 240, 267, 356, 445, 480, 534, 712, 890, 1068, 1335, 1424, 1780, 2136, 2670, 2848, 3560, 4272, 5340, 7120, 8544, 10680, 14240, 21360, 42720.
What is 42720 in binary?
1010011011100000 (hexadecimal A6E0, octal 123340).
What is the square root of 42720?
About 206.6882, exactly 4√2670.
Is 42720 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 42720?
42720 is a Harshad number: divisible by its digit sum 15.