The number 49
49 is a perfect square (7²). Its prime factorisation is . Divisors (3): 1, 7, 49.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 49: a perfect square (7²); a happy number: repeatedly adding the squares of its digits reaches 1; the square of a prime (7²).
- 2
49 is composite. Its prime factorisation is
- 3
The divisors add up to 57; without 49 itself that is 8, so 49 is deficient (8 is less than 49). Euler's totient φ(49) = 42 numbers up to 49 share no factor with it.
- 4
The digits of 49 add up to 13, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 49 = 7^{2} \]49 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 3 |
| Sum of divisors | 57 |
| Euler totient φ(n) | 42 |
| Square | 2401 |
| Cube | 117649 |
| Square root | 7 |
| Digit sum / digital root | 13 / 4 |
| Collatz steps to 1 | 24 |
| Scientific notation | 4.9 × |
| Perfect power |
49 in other forms
| Form | Value |
|---|---|
| In words | forty-nine |
| Roman numerals | XLIX |
| Binary (base 2) | 110001 |
| Octal (base 8) | 61 |
| Hexadecimal (base 16) | 31 |
| Base 3 | 1211 |
| As time | 49 seconds |
Is 49 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 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (49 ÷ 7 = 7) | 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 1) | 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 9) | 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 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 49 a prime number?
No. 49 = , so it is divisible by 7.
What are the factors of 49?
1, 7, 49.
What is 49 in binary?
110001 (hexadecimal 31, octal 61).
What is the square root of 49?
7, because 7 × 7 = 49.
What is 49 in Roman numerals?
XLIX.
Is 49 divisible by 3?
No. Its digits add up to 13, which is not a multiple of 3.
What is special about the number 49?
49 is a perfect square (7²); a happy number: repeatedly adding the squares of its digits reaches 1; the square of a prime (7²).