126
CXXVI
1111110
The number 126 — factors and divisors
Abundant
126 = 2 × 3² × 7. It has 12 divisors, adding up to 312.
Its divisors, itself excluded, add up to more than the number.
Laid out as dots
It fits as 9 × 14. The more divisors, the closer to a square.
- Prime factors
- 2 × 3² × 7
- Divisors
- 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
- Sum of divisors
- 312
- Sum without itself
- 186
- Coprime below it
- 36
- Digit sum
- 9
- Digital root
- 9
- Roman numeral
- CXXVI
- Binary
- 1111110
- Octal
- 176
- Hexadecimal
- 7E
- Base 36
- 3I
- Bits
- 7 bits
- Collatz steps
- 108 steps · peaks at 9,232
- Prime before
- 113
- Prime after
- 127
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 126 a prime number?
No. It breaks down into 2 × 3² × 7.
Q. What are the divisors of 126?
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 — 12 divisors in all, adding up to 312.
Q. How is 126 written in binary?
1111110, which is 7 bits. In hexadecimal it is 7E.
Q. How many Collatz steps does 126 take?
It reaches 1 in 108, peaking at 9,232 on the way.