Question

Etta writes down a prime decomposition of 136 as 2a x b calculate the values of a and b

Answer 1

To find the prime decomposition of 136 as 2^a x b, we repeatedly divide by 2 to get 2^3 x 17, which yields a = 3 and b = 17.

Step-by-step explanation:

When Etta writes down the prime decomposition of 136 as 2a x b, to calculate the values of a and b, we must first find all the prime factors of 136. Since 136 is an even number, we can continuously divide by 2 (which is the smallest prime number) until we can no longer do so. Let's perform the decomposition step by step:

• 136 ÷ 2 = 68
• 68 ÷ 2 = 34
• 34 ÷ 2 = 17

Now, we have reached 17, which is a prime number and cannot be divided further by 2. So we have divided by 2 a total of 3 times (23), and we are left with the prime number 17. Hence, we can write the prime decomposition of 136 as 23 x 17, which gives us a = 3 and b = 17.

Answer 2

The prime decomposition of 136 is 2^a x b. The values of a and b are 3 and 17, respectively.

Step-by-step explanation:

The prime decomposition of 136 can be written as 2a x b. We need to find the values of a and b. To do this, we need to find the prime factorization of 136. We start by dividing 136 by the smallest prime number, which is 2, and we get 68. Then we divide 68 by 2 again and get 34. Continuing this process, we find that the prime factorization of 136 is 2 x 2 x 2 x 17. Therefore, a = 3 and b = 17.