The number 975
975 is a binary palindrome (1111001111). Its prime factorisation is 3 × × 13. Divisors (12): 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 975: a binary palindrome (1111001111).
- 2
975 is composite. Its prime factorisation is
- 3
The divisors add up to 1736; without 975 itself that is 761, so 975 is deficient (761 is less than 975). Euler's totient φ(975) = 480 numbers up to 975 share no factor with it.
- 4
The digits of 975 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 142 steps to reach 1.
LaTeX source of the formulas on this page
\[ 975 = 3 \times 5^{2} \times 13 \]975 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 1736 |
| Euler totient φ(n) | 480 |
| Square | 950625 |
| Cube | 926859375 |
| Square root | 31.224990 (= 5√39) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 142 |
| Scientific notation | 9.75 × |
975 in other forms
| Form | Value |
|---|---|
| In words | nine hundred and seventy-five |
| Roman numerals | CMLXXV |
| Binary (base 2) | 1111001111 |
| Octal (base 8) | 1717 |
| Hexadecimal (base 16) | 3CF |
| Base 3 | 1100010 |
| As time | 975 seconds = 16 min 15 s |
Is 975 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (975 ÷ 3 = 325) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (975 ÷ 5 = 195) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 7) | 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 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 975 a prime number?
No. 975 = 3 × × 13, so it is divisible by 3.
What are the factors of 975?
1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975.
What is 975 in binary?
1111001111 (hexadecimal 3CF, octal 1717).
What is the square root of 975?
About 31.2250, exactly 5√39.
What is 975 in Roman numerals?
CMLXXV.
Is 975 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 975?
975 is a binary palindrome (1111001111).