138
CXXXVIII
10001010
The number 138 — factors and divisors
Abundant
138 = 2 × 3 × 23. It has 8 divisors, adding up to 288.
Its divisors, itself excluded, add up to more than the number.
Laid out as dots
It fits as 6 × 23. The more divisors, the closer to a square.
- Prime factors
- 2 × 3 × 23
- Divisors
- 1, 2, 3, 6, 23, 46, 69, 138
- Sum of divisors
- 288
- Sum without itself
- 150
- Coprime below it
- 44
- Digit sum
- 12
- Digital root
- 3
- Roman numeral
- CXXXVIII
- Binary
- 10001010
- Octal
- 212
- Hexadecimal
- 8A
- Base 36
- 3U
- Bits
- 8 bits
- Collatz steps
- 15 steps · peaks at 208
- Prime before
- 137
- Prime after
- 139
The grid
Ten per row, twenty rows. The filled cells are primes — you can see the multiples of 2 and 5 drop out in columns.
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Numbers either side
How to read this
- The prime factors are what the number is made of. The count and sum of divisors both follow from them.
- Add the divisors, take the number away, and you get perfect, abundant or deficient.
- The length of the binary form is the bit count. 255 taking eight digits is what a byte is.
- Collatz: halve it if even, triple it and add one if odd. The count is how many moves reach 1.
Frequently asked questions
Q. Is 138 a prime number?
No. It breaks down into 2 × 3 × 23.
Q. What are the divisors of 138?
1, 2, 3, 6, 23, 46, 69, 138 — 8 divisors in all, adding up to 288.
Q. How is 138 written in binary?
10001010, which is 8 bits. In hexadecimal it is 8A.
Q. How many Collatz steps does 138 take?
It reaches 1 in 15, peaking at 208 on the way.