Example 2.47 from Prealgebra, 2.4 Find Multiples and Factors

Find Multiples and Factors: example 2.47

Identify each number as prime or composite:

ⓐ $83$
ⓑ $77$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

ⓐ Test each prime, in order, to see if it is a factor of $83$ , starting with $2,$ as shown. We will stop when the quotient is smaller than the divisor.

Prime	Test	Factor of $83 ?$
$2$	Last digit of $83$ is not $0, 2, 4, 6, or 8 .$	No.
$3$	$8 + 3 = 11,$ and $11$ is not divisible by $3 .$	No.
$5$	The last digit of $83$ is not $5$ or $0 .$	No.
$7$	$83 \div 7 = 11.857 ….$	No.
$11$	$83 \div 11 = 7.545 …$	No.

We can stop when we get to $11$ because the quotient $(7.545…)$ is less than the divisor.

We did not find any prime numbers that are factors of $83,$ so we know $83$ is prime.

ⓑ Test each prime, in order, to see if it is a factor of $77 .$

Prime	Test	Factor of $77 ?$
$2$	Last digit is not $0, 2, 4, 6, or 8 .$	No.
$3$	$7 + 7 = 14,$ and $14$ is not divisible by $3 .$	No.
$5$	the last digit is not $5$ or $0 .$	No.
$7$	$77 \div 7 = 11$	Yes.

Since $77$ is divisible by $7,$ we know it is not a prime number. It is composite.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Identify the number as prime or composite:

$91$

How did it go?