How many positive integers between 5 and 31 a) are divisible by 3? Which integers are these? b) are divisible by 4? Which integers are these? c) are divisible by 3 and by 4? Which integers are these?

Answer:Part (A): There are 9 integers between 5 and 31 which are divisible by 3.Part (B): There are 6 integers between 5 and 31 which are divisible by 4.Part (C): There are 2 integers between 5 and 31 which are divisible by 3 and by 4.Step-by-step explanation:Consider the provided information.Part (A) we need to find how many integers between 5 and 31 are divisible by 3.Between 5 and 31 there are 25 integers.According to quotient rule: [tex]\frac{25}{3} \approx8.33[/tex]That means either 8 or 9 integers are divisible by 3 as 8.33 lies between 8 and 9.The integers are: 6, 9, 12, 15, 18, 21, 24, 27, 30Hence, there are 9 integers between 5 and 31 which are divisible by 3.Part (B) we need to find how many integers between 5 and 31  are divisible by 4.Between 5 and 31 there are 25 integers.According to quotient rule: [tex]\frac{25}{4} \approx6.25[/tex]That means either 6 or 7 integers are divisible by 4, as 6.25 lies between 6 and 7.The integers are: 8, 12, 16, 20, 24, 28Hence, there are 6 integers between 5 and 31 which are divisible by 4.Part (C) we need to find how many integers between 5 and 31 are divisible by 3 and by 4Between 5 and 31 there are 25 integers.Integers should be divisible by 3 and by 4, that means integers should be divisible by 3×4=12.According to quotient rule: [tex]\frac{25}{12} \approx2.08[/tex]That means either 2 or 3 integers are divisible by 3 and by 4 or 12, as 2.08 lies between 2 and 3.The integers are: 12, 24,Hence, there are 2 integers between 5 and 31 which are divisible by 3 and by 4.