The number 138
138 is a composite number with 8 divisors. Its prime factorisation is 2 × 3 × 23. Divisors (8): 1, 2, 3, 6, 23, 46, 69, 138.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
138 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
138 is composite. Its prime factorisation is
- 3
The divisors add up to 288; without 138 itself that is 150, so 138 is abundant (150 is more than 138). Euler's totient φ(138) = 44 numbers up to 138 share no factor with it.
- 4
The digits of 138 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 15 steps to reach 1.
LaTeX source of the formulas on this page
\[ 138 = 2 \times 3 \times 23 \]
138 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 288 |
| Euler totient φ(n) | 44 |
| Square | 19044 |
| Cube | 2628072 |
| Square root | 11.747340 |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 15 |
| Scientific notation | 1.38 × |
138 in other forms
| Form | Value |
|---|---|
| In words | one hundred and thirty-eight |
| Roman numerals | CXXXVIII |
| Binary (base 2) | 10001010 |
| Octal (base 8) | 212 |
| Hexadecimal (base 16) | 8A |
| Base 3 | 12010 |
| As time | 138 seconds = 2 min 18 s |
Is 138 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (138 ÷ 2 = 69) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (138 ÷ 3 = 46) | 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 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (138 ÷ 6 = 23) | 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 2) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | 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 138 a prime number?
No. 138 = 2 × 3 × 23, so it is divisible by 2.
What are the factors of 138?
1, 2, 3, 6, 23, 46, 69, 138.
What is 138 in binary?
10001010 (hexadecimal 8A, octal 212).
What is the square root of 138?
About 11.7473.
What is 138 in Roman numerals?
CXXXVIII.
Is 138 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 138?
It is a composite number with 8 divisors.