## q: y (Prime Factors)

The prime factorization of integer y

• the same as (3 p: y). See Primes (p:)

```   q: 2^31
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
q: 1+ 2^31
3 715827883
q: 2+ 2^31
2 5 5 13 41 61 1321```

### Common uses

Mathematical investigations.

## x q: y (Prime Exponents)

The exponents of the first x primes in the factorization of y

• an exponent of 0 means that the corresponding prime is not a factor of y

```   p: i.10   NB. the first 10 primes
2 3 5 7 11 13 17 19 23 29
q: 700    NB. prime factors of 700
2 2 5 5 7

10 q: 700
2 0 2 1 0 0 0 0 0 0
NB. --meaning: 2 twice, 5 twice, 7 once.```

If x=_ then trailing 0s are dropped (i.e. non-factors are omitted)

```   _ q: 700
2 0 2 1```

If x<0 then

• returns a table of primes and their exponents, not just exponents
• the last |x primes are used, and non-factors are omitted.

```   ] y=: 2*3*4*5*6*7*8*9*10*11*12*13*14
87178291200

_5 q: y
3 5 7 11 13
5 2 2  1  1
_6 q: y
2 3 5 7 11 13
11 5 2 2  1  1
_7 q: y
2 3 5 7 11 13
11 5 2 2  1  1```

If x=__ then just sufficient primes are shown

• the same as (2 p: y). See Primes (p:)

```   __ q: y
2 3 5 7 11 13
11 5 2 2  1  1```

### Common uses

Mathematical investigations.