The number 78420
78420 is a composite number with 24 divisors. Its prime factorisation is × 3 × 5 × 1307. Divisors (24): 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 1307, 2614, 3921, 5228 … 78420.
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How to work it out
- 1
What is special about 78420: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
78420 is composite. Its prime factorisation is
- 3
The divisors add up to 219744; without 78420 itself that is 141324, so 78420 is abundant (141324 is more than 78420). Euler's totient φ(78420) = 20896 numbers up to 78420 share no factor with it.
- 4
The digits of 78420 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 78420 = 2^{2} \times 3 \times 5 \times 1307 \]78420 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 219744 |
| Euler totient φ(n) | 20896 |
| Square | 6149696400 |
| Cube | 482259191688000 |
| Square root | 280.035712 (= 2√19605) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 138 |
| Scientific notation | 7.842 × |
78420 in other forms
| Form | Value |
|---|---|
| In words | seventy-eight thousand four hundred and twenty |
| Binary (base 2) | 10011001001010100 |
| Octal (base 8) | 231124 |
| Hexadecimal (base 16) | 13254 |
| Base 3 | 10222120110 |
| As time | 78420 seconds = 21 h 47 min 0 s |
Is 78420 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (78420 ÷ 2 = 39210) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (78420 ÷ 3 = 26140) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (78420 ÷ 4 = 19605) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (78420 ÷ 5 = 15684) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (78420 ÷ 6 = 13070) | 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 | 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 (78420 ÷ 10 = 7842) | 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 (78420 ÷ 12 = 6535) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 78420 a prime number?
No. 78420 = × 3 × 5 × 1307, so it is divisible by 2.
What are the factors of 78420?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 1307, 2614, 3921, 5228, 6535, 7842, 13070, 15684, 19605, 26140, 39210, 78420.
What is 78420 in binary?
10011001001010100 (hexadecimal 13254, octal 231124).
What is the square root of 78420?
About 280.0357, exactly 2√19605.
Is 78420 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 78420?
78420 is a happy number: repeatedly adding the squares of its digits reaches 1.