Question
(d) Is 1774 prime? If not, state the smallest prime number by which 1774 is divisible. Select the correct choice below, and if necessary, fill in the answer box within your choice. A. The number is not prime. The smallest prime number that it is divisible by is B. The number is prime.
Ask by Zimmerman Valdez. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The number 1774 is not prime. The smallest prime number that divides it is 2.
Solution
We test whether 1774 is prime by checking divisibility by the smallest primes.
- First, check divisibility by 2. Since \(1774\) is even, it is divisible by 2:
\[
1774 \div 2 = 887.
\]
- This shows that
\[
1774 = 2 \times 887.
\]
- Since 2 is a prime factor and it divides 1774, the number is not prime.
Thus, the correct choice is:
A. The number is not prime. The smallest prime number that it is divisible by is \(2\).
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Simplify this solution The Deep Dive
A. The number is not prime. The smallest prime number that it is divisible by is 2. This is because 1774 is an even number, and any even number greater than 2 can always be divided by 2, which makes it composite rather than prime. To double-check, you can divide 1774 by 2, and you'll find that 1774 = 2 x 887, confirming its composite nature!
