The number 34720
34720 is a composite number with 48 divisors. Its prime factorisation is × 5 × 7 × 31. Divisors (48): 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 31, 32, 35, 40, 56 … 34720.
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How to work it out
- 1
What is special about 34720: a Harshad number: divisible by its digit sum 16.
- 2
34720 is composite. Its prime factorisation is
- 3
The divisors add up to 96768; without 34720 itself that is 62048, so 34720 is abundant (62048 is more than 34720). Euler's totient φ(34720) = 11520 numbers up to 34720 share no factor with it.
- 4
The digits of 34720 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 34720 = 2^{5} \times 5 \times 7 \times 31 \]34720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 96768 |
| Euler totient φ(n) | 11520 |
| Square | 1205478400 |
| Cube | 41854210048000 |
| Square root | 186.333035 (= 4√2170) |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 49 |
| Scientific notation | 3.472 × |
34720 in other forms
| Form | Value |
|---|---|
| In words | thirty-four thousand seven hundred and twenty |
| Binary (base 2) | 1000011110100000 |
| Octal (base 8) | 103640 |
| Hexadecimal (base 16) | 87A0 |
| Base 3 | 1202121221 |
| As time | 34720 seconds = 9 h 38 min 40 s |
Is 34720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (34720 ÷ 2 = 17360) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (34720 ÷ 4 = 8680) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (34720 ÷ 5 = 6944) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (34720 ÷ 7 = 4960) | 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 (34720 ÷ 8 = 4340) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (34720 ÷ 10 = 3472) | 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 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 34720 a prime number?
No. 34720 = × 5 × 7 × 31, so it is divisible by 2.
What are the factors of 34720?
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 31, 32, 35, 40, 56, 62, 70, 80, 112, 124, 140, 155, 160, 217, 224, 248, 280, 310, 434, 496, 560, 620, 868, 992, 1085, 1120, 1240, 1736, 2170, 2480, 3472, 4340, 4960, 6944, 8680, 17360, 34720.
What is 34720 in binary?
1000011110100000 (hexadecimal 87A0, octal 103640).
What is the square root of 34720?
About 186.3330, exactly 4√2170.
Is 34720 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 34720?
34720 is a Harshad number: divisible by its digit sum 16.