The number 72420
72420 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 17 × 71. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68 … 72420.
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How to work it out
- 1
What is special about 72420: a Harshad number: divisible by its digit sum 15.
- 2
72420 is composite. Its prime factorisation is
- 3
The divisors add up to 217728; without 72420 itself that is 145308, so 72420 is abundant (145308 is more than 72420). Euler's totient φ(72420) = 17920 numbers up to 72420 share no factor with it.
- 4
The digits of 72420 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 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72420 = 2^{2} \times 3 \times 5 \times 17 \times 71 \]72420 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 217728 |
| Euler totient φ(n) | 17920 |
| Square | 5244656400 |
| Cube | 379818016488000 |
| Square root | 269.109643 (= 2√18105) |
| Digit sum / digital root | 15 / 6 |
| Collatz steps to 1 | 42 |
| Scientific notation | 7.242 × |
72420 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand four hundred and twenty |
| Binary (base 2) | 10001101011100100 |
| Octal (base 8) | 215344 |
| Hexadecimal (base 16) | 11AE4 |
| Base 3 | 10200100020 |
| As time | 72420 seconds = 20 h 7 min 0 s |
Is 72420 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72420 ÷ 2 = 36210) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72420 ÷ 3 = 24140) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72420 ÷ 4 = 18105) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (72420 ÷ 5 = 14484) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72420 ÷ 6 = 12070) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (72420 ÷ 10 = 7242) | 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 (72420 ÷ 12 = 6035) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72420 a prime number?
No. 72420 = × 3 × 5 × 17 × 71, so it is divisible by 2.
What are the factors of 72420?
1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 71, 85, 102, 142, 170, 204, 213, 255, 284, 340, 355, 426, 510, 710, 852, 1020, 1065, 1207, 1420, 2130, 2414, 3621, 4260, 4828, 6035, 7242, 12070, 14484, 18105, 24140, 36210, 72420.
What is 72420 in binary?
10001101011100100 (hexadecimal 11AE4, octal 215344).
What is the square root of 72420?
About 269.1096, exactly 2√18105.
Is 72420 divisible by 3?
Yes. Its digits add up to 15, a multiple of 3.
What is special about the number 72420?
72420 is a Harshad number: divisible by its digit sum 15.