Question

Use the unique factorization theorem to write the integer in standard factored form. 1.5400

Answer 1

Answer:

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