Question

relating factors and multiples i - item 33493
the factor rainbow for the number 48 is shown.
which two factor pairs of 48 contain a factor that is a prime number?
1 and 48
2 and 24
3 and 16
4 and 12
6 and 8

Explanation:

Step1: Recall Prime Number Definition

A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. So we check each factor pair:

Step2: Analyze "1 and 48"

1 is not a prime number (by definition, primes are >1), and 48 is composite. So this pair has no prime factor.

Step3: Analyze "2 and 24"

2 is a prime number (divisors 1 and 2). So this pair has a prime factor.

Step4: Analyze "3 and 16"

3 is a prime number (divisors 1 and 3). So this pair has a prime factor.

Step5: Analyze "4 and 12"

4 (divisors 1,2,4) and 12 (divisors 1,2,3,4,6,12) are composite. No prime factor.

Step6: Analyze "6 and 8"

6 (divisors 1,2,3,6) and 8 (divisors 1,2,4,8) are composite. No prime factor.

Answer:

The two factor pairs are:

• 2 and 24
• 3 and 16