Question

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

a. 4,116
b. 1,617
c.2,205

Answer 1

a. 4,116 = 2^2 × 3 × 7 × 41 b. 1,617 = 3 × 7^2 × 11 c. 2,205 = 3 × 5 × 7 × 11

Step-by-step explanation:

a. To write 4,116 in standard factored form using the unique factorization theorem, we need to find the prime factors of the number. 4,116 can be factored as 2 × 2 × 3 × 7 × 41. Therefore, the standard factored form of 4,116 is 2^2 × 3 × 7 × 41.

b. To write 1,617 in standard factored form, we need to find the prime factors. 1,617 can be factored as 3 × 7 × 7 × 11. Therefore, the standard factored form of 1,617 is 3 × 7^2 × 11.

c. To write 2,205 in standard factored form, we need to find the prime factors. 2,205 can be factored as 3 × 5 × 7 × 11. Therefore, the standard factored form of 2,205 is 3 × 5 × 7 × 11.

Answer 2

To write integers in standard factored form using the unique factorization theorem, we need to express the integers as a product of their prime factors. We can use prime factorization to factorize the given integers a. 4,116, b. 1,617, and c. 2,205.

Step-by-step explanation:

To write integers in standard factored form using the unique factorization theorem, we need to express the integers as a product of their prime factors. Let's solve the given questions step-by-step:

a) To factorize 4,116, we start by dividing it by its smallest prime factor, which is 2. We get 2 × 2 × 3 × 7 × 31. So, the standard factored form of 4,116 is 2^2 × 3 × 7 × 31.

b) To factorize 1,617, we divide it by 3, since it is divisible by 3. We get 3 × 3 × 13 × 11. So, the standard factored form of 1,617 is 3^2 × 13 × 11.

c) To factorize 2,205, we divide it by 3, as it is divisible by 3. We get 3 × 5 × 7 × 11. So, the standard factored form of 2,205 is 3 × 5 × 7 × 11.