The number 77970
77970 is a composite number with 32 divisors. Its prime factorisation is 2 × 3 × 5 × 23 × 113. Divisors (32): 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 113, 115, 138, 226, 230 … 77970.
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How to work it out
- 1
What is special about 77970: a Harshad number: divisible by its digit sum 30.
- 2
77970 is composite. Its prime factorisation is
- 3
The divisors add up to 196992; without 77970 itself that is 119022, so 77970 is abundant (119022 is more than 77970). Euler's totient φ(77970) = 19712 numbers up to 77970 share no factor with it.
- 4
The digits of 77970 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 200 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77970 = 2 \times 3 \times 5 \times 23 \times 113 \]
77970 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 196992 |
| Euler totient φ(n) | 19712 |
| Square | 6079320900 |
| Cube | 474004650573000 |
| Square root | 279.231087 |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 200 |
| Scientific notation | 7.797 × |
77970 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and seventy |
| Binary (base 2) | 10011000010010010 |
| Octal (base 8) | 230222 |
| Hexadecimal (base 16) | 13092 |
| Base 3 | 10221221210 |
| As time | 77970 seconds = 21 h 39 min 30 s |
Is 77970 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77970 ÷ 2 = 38985) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77970 ÷ 3 = 25990) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77970 ÷ 5 = 15594) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77970 ÷ 6 = 12995) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 2) | 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 (77970 ÷ 10 = 7797) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77970 a prime number?
No. 77970 = 2 × 3 × 5 × 23 × 113, so it is divisible by 2.
What are the factors of 77970?
1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 113, 115, 138, 226, 230, 339, 345, 565, 678, 690, 1130, 1695, 2599, 3390, 5198, 7797, 12995, 15594, 25990, 38985, 77970.
What is 77970 in binary?
10011000010010010 (hexadecimal 13092, octal 230222).
What is the square root of 77970?
About 279.2311.
Is 77970 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 77970?
77970 is a Harshad number: divisible by its digit sum 30.