Use the unique factorization theorem to write the integer in standard factored form.

1.5400

Standard factor form of the integer : 15400 = 2³ * 5² * 7 * 11

Step-by-step explanation:

According to the unique factorization theorem, a given integer n (where, n>1), either is a prime number or can be represented as the product of the prime numbers.

Firstly, it is checked that the given integer is divisible by the smallest prime number 2. If the integer is not divisible by 2, then the integer is checked for the next prime number 3 and then checked for 5 and so on until the remaining integers are prime numbers.

So, the standard factored form of the integer:

15400 = 2 * 770

15400 = 2 * 2 * 3850

15400 = 2 * 2 * 2 * 1925

15400 = 2 * 2 * 2 * 5 * 385

15400 = 2 * 2 * 2 * 5 * 5 * 77

15400 = 2 * 2 * 2 * 5 * 5 * 7 * 11

or,

15400 = 2³ * 5² * 7 * 11

Therefore, the standard factor form of the integer: 15400 = 2³ * 5² * 7 * 11