The number 77952
77952 is a composite number with 64 divisors. Its prime factorisation is × 3 × 7 × 29. Divisors (64): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 32, 42 … 77952.
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How to work it out
- 1
What is special about 77952: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77952 is composite. Its prime factorisation is
- 3
The divisors add up to 244800; without 77952 itself that is 166848, so 77952 is abundant (166848 is more than 77952). Euler's totient φ(77952) = 21504 numbers up to 77952 share no factor with it.
- 4
The digits of 77952 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 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77952 = 2^{7} \times 3 \times 7 \times 29 \]77952 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 244800 |
| Euler totient φ(n) | 21504 |
| Square | 6076514304 |
| Cube | 473676443025408 |
| Square root | 279.198854 (= 8√1218) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 138 |
| Scientific notation | 7.7952 × |
77952 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and fifty-two |
| Binary (base 2) | 10011000010000000 |
| Octal (base 8) | 230200 |
| Hexadecimal (base 16) | 13080 |
| Base 3 | 10221221010 |
| As time | 77952 seconds = 21 h 39 min 12 s |
Is 77952 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77952 ÷ 2 = 38976) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77952 ÷ 3 = 25984) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77952 ÷ 4 = 19488) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77952 ÷ 6 = 12992) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (77952 ÷ 7 = 11136) | 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 (77952 ÷ 8 = 9744) | 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 | No (remainder 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77952 ÷ 12 = 6496) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77952 a prime number?
No. 77952 = × 3 × 7 × 29, so it is divisible by 2.
What are the factors of 77952?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 32, 42, 48, 56, 58, 64, 84, 87, 96, 112, 116, 128, 168, 174, 192, 203, 224, 232, 336, 348, 384, 406, 448, 464, 609, 672, 696, 812, 896, 928, 1218, 1344, 1392, 1624, 1856, 2436, 2688, 2784, 3248, 3712, 4872, 5568, 6496, 9744, 11136, 12992, 19488, 25984, 38976, 77952.
What is 77952 in binary?
10011000010000000 (hexadecimal 13080, octal 230200).
What is the square root of 77952?
About 279.1989, exactly 8√1218.
Is 77952 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 77952?
77952 is a happy number: repeatedly adding the squares of its digits reaches 1.