) Find all prime numbers that divide 40! (recall that 40! = 1 · 2 · 3 · 4 · · · 40). (b) Find the prime factorization of the integers 1234; 10,140; and 36,000.

Respuesta :

Answer:

a) [tex]2,3,5,7,11,13,17,19,23,29,31,37[/tex]

b) Prime factorization

Step-by-step explanation:

a) prime numbers that divide 40!

[tex]40! = 40\times 39\times 38\times ... \imes 3\times 2\times 1[/tex]

Thus, the prime number that divides 40! are all the prime number from 1 to 40.

Prime numbers that divide 40! =

[tex]2,3,5,7,11,13,17,19,23,29,31,37[/tex]

b) Prime factorization:

It is the process of expressing the composite number as a product of prime numbers.

[tex]1234 = 617\times 2\\10=5\times 2\\140=7\times 5\times 2\times 2\\36000 = 5^3\times 3^2\times 2^5[/tex]