What is the prime factorization of 160 in exponent form?
The correct answer and explanation is:
The prime factorization of 160 in exponent form is:
160 = 2^5 × 5^1
Explanation:
To find the prime factorization of a number means to express it as a product of prime numbers raised to their respective powers.
Start with 160 and divide it by the smallest prime number possible, which is 2:
- 160 ÷ 2 = 80
- 80 ÷ 2 = 40
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
At this point, 5 is no longer divisible by 2, so move to the next smallest prime number, which is 3. Since 5 is not divisible by 3, move to the next prime number, which is 5 itself:
- 5 ÷ 5 = 1
Now, since the division resulted in 1, the factorization process is complete.
Count how many times 2 was used as a factor. It was used 5 times (2 × 2 × 2 × 2 × 2). The prime 5 was used once.
Thus, the prime factors are:
- 2 raised to the power of 5, written as 2^5
- 5 raised to the power of 1, written as 5^1
Multiplying these prime factors confirms the original number:
2^5 × 5^1 = 32 × 5 = 160
This method ensures the number is broken down into its simplest building blocks—prime numbers. Expressing the factorization in exponent form is a concise way to represent repeated multiplication of the same prime number.