Final answer:
The pairs of numbers that have the same greatest common factor (GCF) are 26 and 38, and 22 and 34.
Step-by-step explanation:
To determine the pairs of numbers that have the same greatest common factor (GCF), we need to find the GCF for each pair and compare them. The GCF is the largest positive integer that divides evenly into both numbers. Let's look at each pair:
a. 16 and 30: The prime factors of 16 are 2 * 2 * 2 * 2, and the prime factors of 30 are 2 * 3 * 5. The GCF is the product of the common prime factors, which is 2. So this pair does not have the same GCF.
b. 26 and 38: The prime factors of 26 are 2 * 13, and the prime factors of 38 are 2 * 19. The GCF is the product of the common prime factors, which is 2. So this pair does have the same GCF.
c. 12 and 28: The prime factors of 12 are 2 * 2 * 3, and the prime factors of 28 are 2 * 2 * 7. The GCF is the product of the common prime factors, which is 2 * 2 = 4. So this pair does not have the same GCF.
d. 22 and 34: The prime factors of 22 are 2 * 11, and the prime factors of 34 are 2 * 17. The GCF is the product of the common prime factors, which is 2. So this pair does have the same GCF.
e. 24 and 32: The prime factors of 24 are 2 * 2 * 2 * 3, and the prime factors of 32 are 2 * 2 * 2 * 2 * 2. The GCF is the product of the common prime factors, which is 2 * 2 * 2 = 8. So this pair does not have the same GCF.
Therefore, the pairs of numbers that have the same GCF are: b. 26 and 38 and d. 22 and 34.