Question

Determine whether each of these integers is prime.

a) 21 b) 29

c) 71 d) 97

e) 111 f) 143

Short answer

a) Not prime b) Prime c) Prime

d) Prime e) Not prime f) Not prime.

Step-by-step solution

Step 1:

An integer $p$larger than x is called prime if the only positive factors of $p$are 1 and$p$

a) Factorize the given integer.

_{$21=3\times 7$}

Since the factors are not only 1 and 21,21 is not prime.

Step 2:

b) Factorize the given integer.

$29=1\times 29$

Since the factors are only 1 and 29, 29 is prime.

c) Factorize the given integer.

_{$71=1\times 71$}

Since the factors are only 1 and 71, 71 is prime.

Step 3:

d) Factorize the given integer.

_{$97=1\times 97$}

Since the factors are only 1 and 97, 97 is prime.

e) Factorize the given integer.

_{$111=3\times 37$}

Since the factors are not only 1 and 111, 111 is not prime.

f) Factorize the given integer.

$143=11\times 13$

Since the factors are not only 1 and 143, 143 is not prime.