Is 437 a prime number? If not, give its factorization into prime numbers. Not a prime number. The factors of 437 are 1, 19, and 23. (3 pts) Is 151 a prime number? If not, give its factorization into prime numbers. Prime number. (2 pts) Is 51 a prime number? If not, give its factorization into prime numbers. Not a prime number. The factors of 51 are 1, 3, 17, and 51.
The Correct Answer and Explanation is:
prime factorization is 19 × 23.
**b. Is 151 a prime number?Here are the correct answers and a detailed explanation for each question.
a. Is 437 a prime number? If not, give its factorization into prime numbers.
No, 437 is not a prime number. Its factorization into prime numbers is 19 × 23.
b. Is 151 a prime number? If not, give its factorization into prime numbers.
Yes, If not, give its factorization into prime numbers.**
Yes, 151 is a prime number.
**151 is a prime number.
c. Is 51 a prime number? If not, give its factorization into prime numbers.
No, 51 is not a prime number. Its factorization into prime numbers isc. Is 51 a prime number? If not, give its factorization into prime numbers.**
No, 3 × 17.
Explanation
A prime number is a natural number greater than 1 that has51 is not a prime number. Its prime factorization is 3 × 17.
Explanation
exactly two distinct positive divisors: 1 and itself. A number that is not prime is called a composite number. To determine if aA prime number is a whole number greater than 1 that has only two factors: 1 and itself. A number number is prime, the most common method is trial division. We check for divisibility by prime numbers starting from 2. that has more than two factors is called a composite number. Every composite number can be expressed as a unique product of prime A key optimization is that we only need to test for prime divisors up to the square root of the number in question. If no numbers, a process called prime factorization.
To determine if a number is prime, we can use a method called trial division prime factor is found within this range, the number is prime.
a. Analysis of 437. This involves testing whether the number is evenly divisible by any prime number smaller than or equal to its square root. If
To determine if 437 is prime, we find its square root, which is approximately 20.9 it is not divisible by any of these smaller primes, then the number is prime.
a. Analysis of 43. We then test for divisibility by all prime numbers up to 19, which are 2, 3,7
To check if 437 is prime, we find its square root, which is approximately 20.9 5, 7, 11, 13, 17, and 19.
- 437 is not divisible by 2 (it is odd).
- The sum of its digits. We then test for divisibility by prime numbers up to 19 (2, 3, 5, (4+3+7=14) is not divisible by 3.
- It does not end in7, 11, 13, 17, 19). While testing, we find that 0 or 5, so it is not divisible by 5.
- Dividing by 7,437 can be divided evenly by 19. The result of this division is 23 (43 11, 13, and 17 leaves a remainder.
- When we test 17 ÷ 19 = 23). Since both 19 and 23 are themselves prime numbers, we9, we find that 437 ÷ 19 = 23.
Since 437 can have found the prime factorization of 437. Therefore, 437 is a composite number.
** be divided by 19 and 23, it is not a prime number. Both 19 and b. Analysis of 151**
For the number 151, its square root is approximately 12.23 are themselves prime numbers, so the prime factorization of 437 is 19 × 23.
3. The prime numbers we need to test are 2, 3, 5, 7, and b. Analysis of 151
To check if 151 is prime, we find its square root, which11.
- 151 is not divisible by 2 because it is an odd number.
- It is not divisible by 3 because the sum of its digits (1 + 5 + 1 = 7) is approximately 12.3. We only need to test the prime numbers up to 11: 2, 3, 5, 7, and 11.
- 151 is not divisible by is not a multiple of 3.
- It is not divisible by 5 because its last digit is not2, 3, or 5.
- 151 ÷ 7 = 21 with a remainder 0 or 5.
- It is not divisible by 7 or 11 (151 ÷ of 4.
- 151 ÷ 11 = 13 with a remainder of 8 7 = 21 remainder 4; 151 ÷ 11 = 13 remainder 8).
.
Since 151 is not divisible by any prime number less than or equal to its square root, weSince 151 is not divisible by any prime number up to its square root, it is a prime number.
**c can conclude that 151 is a prime number.
c. Analysis of 51
To. Analysis of 51**
The square root of 51 is approximately 7.1. We only determine if 51 is prime, we find its square root, which is approximately 7.1. We need to need to test the prime numbers 2, 3, 5, and 7. The number 51 is odd test the primes 2, 3, 5, and 7.
- 51 is not divisible, so it is not divisible by 2. However, the sum of its digits (5 + 1 = by 2.
- The sum of its digits (5+1=6) is divisible by 3, which6) is divisible by 3, which means 51 is also divisible by 3. Performing the division, means 51 is also divisible by 3.
- 51 ÷ 3 = 17.
Since we get 51 ÷ 3 = 17. Both 3 and 17 are prime numbers, so 51 has factors other than 1 and itself, it is not a prime number. Its prime factors are 51 is a composite number.3 and 17, making its prime factorization 3 × 17.
