The number 77972
77972 is a composite number with 12 divisors. Its prime factorisation is × 101 × 193. Divisors (12): 1, 2, 4, 101, 193, 202, 386, 404, 772, 19493, 38986, 77972.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
77972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77972 is composite. Its prime factorisation is
- 3
The divisors add up to 138516; without 77972 itself that is 60544, so 77972 is deficient (60544 is less than 77972). Euler's totient φ(77972) = 38400 numbers up to 77972 share no factor with it.
- 4
The digits of 77972 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77972 = 2^{2} \times 101 \times 193 \]77972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 138516 |
| Euler totient φ(n) | 38400 |
| Square | 6079632784 |
| Cube | 474041127434048 |
| Square root | 279.234668 (= 2√19493) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.7972 × |
77972 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and seventy-two |
| Binary (base 2) | 10011000010010100 |
| Octal (base 8) | 230224 |
| Hexadecimal (base 16) | 13094 |
| Base 3 | 10221221212 |
| As time | 77972 seconds = 21 h 39 min 32 s |
Is 77972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77972 ÷ 2 = 38986) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77972 ÷ 4 = 19493) | 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 2) | 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 5) | 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 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77972 a prime number?
No. 77972 = × 101 × 193, so it is divisible by 2.
What are the factors of 77972?
1, 2, 4, 101, 193, 202, 386, 404, 772, 19493, 38986, 77972.
What is 77972 in binary?
10011000010010100 (hexadecimal 13094, octal 230224).
What is the square root of 77972?
About 279.2347, exactly 2√19493.
Is 77972 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 77972?
It is a composite number with 12 divisors.