The number 77872
77872 is a composite number with 20 divisors. Its prime factorisation is × 31 × 157. Divisors (20): 1, 2, 4, 8, 16, 31, 62, 124, 157, 248, 314, 496, 628, 1256, 2512, 4867 … 77872.
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How to work it out
- 1
What is special about 77872: a Harshad number: divisible by its digit sum 31.
- 2
77872 is composite. Its prime factorisation is
- 3
The divisors add up to 156736; without 77872 itself that is 78864, so 77872 is abundant (78864 is more than 77872). Euler's totient φ(77872) = 37440 numbers up to 77872 share no factor with it.
- 4
The digits of 77872 add up to 31, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77872 = 2^{4} \times 31 \times 157 \]77872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 156736 |
| Euler totient φ(n) | 37440 |
| Square | 6064048384 |
| Cube | 472219575758848 |
| Square root | 279.055550 (= 4√4867) |
| Digit sum / digital root | 31 / 4 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.7872 × |
77872 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand eight hundred and seventy-two |
| Binary (base 2) | 10011000000110000 |
| Octal (base 8) | 230060 |
| Hexadecimal (base 16) | 13030 |
| Base 3 | 10221211011 |
| As time | 77872 seconds = 21 h 37 min 52 s |
Is 77872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77872 ÷ 2 = 38936) | 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 (77872 ÷ 4 = 19468) | 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 | No (remainder 4) | 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 | Yes (77872 ÷ 8 = 9734) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 3) | 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 77872 a prime number?
No. 77872 = × 31 × 157, so it is divisible by 2.
What are the factors of 77872?
1, 2, 4, 8, 16, 31, 62, 124, 157, 248, 314, 496, 628, 1256, 2512, 4867, 9734, 19468, 38936, 77872.
What is 77872 in binary?
10011000000110000 (hexadecimal 13030, octal 230060).
What is the square root of 77872?
About 279.0556, exactly 4√4867.
Is 77872 divisible by 3?
No. Its digits add up to 31, which is not a multiple of 3.
What is special about the number 77872?
77872 is a Harshad number: divisible by its digit sum 31.