The number 1972
1972 is a composite number with 12 divisors. Its prime factorisation is × 17 × 29. Divisors (12): 1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 986, 1972.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
1972 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
1972 is composite. Its prime factorisation is
- 3
The divisors add up to 3780; without 1972 itself that is 1808, so 1972 is deficient (1808 is less than 1972). Euler's totient φ(1972) = 896 numbers up to 1972 share no factor with it.
- 4
The digits of 1972 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1972 = 2^{2} \times 17 \times 29 \]1972 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 3780 |
| Euler totient φ(n) | 896 |
| Square | 3888784 |
| Cube | 7668682048 |
| Square root | 44.407207 (= 2√493) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 50 |
| Scientific notation | 1.972 × |
1972 in other forms
| Form | Value |
|---|---|
| In words | one thousand nine hundred and seventy-two |
| Roman numerals | MCMLXXII |
| Binary (base 2) | 11110110100 |
| Octal (base 8) | 3664 |
| Hexadecimal (base 16) | 7B4 |
| Base 3 | 2201001 |
| As time | 1972 seconds = 32 min 52 s |
Is 1972 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (1972 ÷ 2 = 986) | 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 (1972 ÷ 4 = 493) | 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 5) | 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 1) | 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 1972 a prime number?
No. 1972 = × 17 × 29, so it is divisible by 2.
What are the factors of 1972?
1, 2, 4, 17, 29, 34, 58, 68, 116, 493, 986, 1972.
What is 1972 in binary?
11110110100 (hexadecimal 7B4, octal 3664).
What is the square root of 1972?
About 44.4072, exactly 2√493.
What is 1972 in Roman numerals?
MCMLXXII.
Is 1972 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 1972?
It is a composite number with 12 divisors.