45
XLV
101101
The number 45 — factors and divisors
Deficient
45 = 3² × 5. It has 6 divisors, adding up to 78.
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 5 × 9. The more divisors, the closer to a square.
- Prime factors
- 3² × 5
- Divisors
- 1, 3, 5, 9, 15, 45
- Sum of divisors
- 78
- Sum without itself
- 33
- Coprime below it
- 24
- Digit sum
- 9
- Digital root
- 9
- Roman numeral
- XLV
- Binary
- 101101
- Octal
- 55
- Hexadecimal
- 2D
- Base 36
- 19
- Bits
- 6 bits
- Collatz steps
- 16 steps · peaks at 136
- Prime before
- 43
- Prime after
- 47
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 45 a prime number?
No. It breaks down into 3² × 5.
Q. What are the divisors of 45?
1, 3, 5, 9, 15, 45 — 6 divisors in all, adding up to 78.
Q. How is 45 written in binary?
101101, which is 6 bits. In hexadecimal it is 2D.
Q. How many Collatz steps does 45 take?
It reaches 1 in 16, peaking at 136 on the way.