The number 77742
77742 is a composite number with 24 divisors. Its prime factorisation is 2 × × 7 × 617. Divisors (24): 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 617, 1234, 1851, 3702 … 77742.
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How to work it out
- 1
What is special about 77742: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77742 is composite. Its prime factorisation is
- 3
The divisors add up to 192816; without 77742 itself that is 115074, so 77742 is abundant (115074 is more than 77742). Euler's totient φ(77742) = 22176 numbers up to 77742 share no factor with it.
- 4
The digits of 77742 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77742 = 2 \times 3^{2} \times 7 \times 617 \]77742 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 192816 |
| Euler totient φ(n) | 22176 |
| Square | 6043818564 |
| Cube | 469858542802488 |
| Square root | 278.822524 (= 3√8638) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.7742 × |
77742 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand seven hundred and forty-two |
| Binary (base 2) | 10010111110101110 |
| Octal (base 8) | 227656 |
| Hexadecimal (base 16) | 12FAE |
| Base 3 | 10221122100 |
| As time | 77742 seconds = 21 h 35 min 42 s |
Is 77742 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77742 ÷ 2 = 38871) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77742 ÷ 3 = 25914) | 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 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77742 ÷ 6 = 12957) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (77742 ÷ 7 = 11106) | 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 6) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77742 ÷ 9 = 8638) | 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 5) | 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 77742 a prime number?
No. 77742 = 2 × × 7 × 617, so it is divisible by 2.
What are the factors of 77742?
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 617, 1234, 1851, 3702, 4319, 5553, 8638, 11106, 12957, 25914, 38871, 77742.
What is 77742 in binary?
10010111110101110 (hexadecimal 12FAE, octal 227656).
What is the square root of 77742?
About 278.8225, exactly 3√8638.
Is 77742 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 77742?
77742 is a happy number: repeatedly adding the squares of its digits reaches 1.