105
CV
1101001
The number 105 — factors and divisors
Deficient
105 = 3 × 5 × 7. It has 8 divisors, adding up to 192.
Its divisors, itself excluded, add up to less than the number.
Families it belongs to
Triangular
The running total of 1, 2, 3 … — the dots stack into a triangle.
Laid out as dots
It fits as 7 × 15. The more divisors, the closer to a square.
- Prime factors
- 3 × 5 × 7
- Divisors
- 1, 3, 5, 7, 15, 21, 35, 105
- Sum of divisors
- 192
- Sum without itself
- 87
- Coprime below it
- 48
- Digit sum
- 6
- Digital root
- 6
- Roman numeral
- CV
- Binary
- 1101001
- Octal
- 151
- Hexadecimal
- 69
- Base 36
- 2X
- Bits
- 7 bits
- Collatz steps
- 38 steps · peaks at 808
- Prime before
- 103
- Prime after
- 107
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 105 a prime number?
No. It breaks down into 3 × 5 × 7.
Q. What are the divisors of 105?
1, 3, 5, 7, 15, 21, 35, 105 — 8 divisors in all, adding up to 192.
Q. How is 105 written in binary?
1101001, which is 7 bits. In hexadecimal it is 69.
Q. How many Collatz steps does 105 take?
It reaches 1 in 38, peaking at 808 on the way.