3
III
11
The number 3 — factors and divisors
Deficient
3 is a prime: only 1 and itself divide it. The prime before is 2, the next is 5.
Its divisors, itself excluded, add up to less than the number.
Families it belongs to
Prime
Nothing divides it but 1 and itself.
Triangular
The running total of 1, 2, 3 … — the dots stack into a triangle.
Fibonacci
It sits in the run where each number is the sum of the two before it.
Laid out as dots
It only fits in one row. Having no other rectangle is what being prime means.
- Prime factors
- It does not break down further
- Divisors
- 1, 3
- Sum of divisors
- 4
- Sum without itself
- 1
- Coprime below it
- 2
- Digit sum
- 3
- Digital root
- 3
- Roman numeral
- III
- Binary
- 11
- Octal
- 3
- Hexadecimal
- 3
- Base 36
- 3
- Bits
- 2 bits
- Collatz steps
- 7 steps · peaks at 16
- Prime before
- 2
- Prime after
- 5
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.
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200
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 3 a prime number?
Yes. Nothing divides it but 1 and itself.
Q. What are the divisors of 3?
1, 3 — 2 divisors in all, adding up to 4.
Q. How is 3 written in binary?
11, which is 2 bits. In hexadecimal it is 3.
Q. How many Collatz steps does 3 take?
It reaches 1 in 7, peaking at 16 on the way.