1. Determine whether each of these integers is prime.a) 21 b) 29 c) 71 d) 97e) 111 f ) 143 g) 93 h) 1012. Find the prime factorization of each of these integers.a) 39 b) 81 c) 101d) 143 e) 289 f ) 899

1. To determine whether an integer is prime, we need to check if it has only two distinct positive divisors: 1 and itself.

a) 21: It is not a prime number because it can be divided evenly by 1, 3, 7, and 21. b) 29: It is a prime number because it can only be divided evenly by 1 and 29. c) 71: It is a prime number because it can only be divided evenly by 1 and 71. d) 97: It is a prime number because it can only be divided evenly by 1 and 97. e) 111: It is not a prime number because it can be divided evenly by 1, 3, 37, and 111. f) 143: It is not a prime number because it can be divided evenly by 1, 11, 13, and 143. g) 93: It is not a prime number because it can be divided evenly by 1, 3, 31, and 93. h) 101: It is a prime number because it can only be divided evenly by 1 and 101.

2. To find the prime factorization of an integer, we need to divide the number by prime numbers, starting from the smallest (2), and continue the process with the quotient until the quotient is a prime number.

a) 39: The prime factorization is 3 * 13. b) 81: The prime factorization is 3^4. c) 101: The prime factorization is 101 (since 101 is a prime number). d) 143: The prime factorization is 11 * 13. e) 289: The prime factorization is 17^2. f) 899: The prime factorization is 29 * 31.