4 a. What are the first three common multiples of 5 and 8? Answer: 40, 80, 120 b. List the common factors of 24 and 32. Answer: 1, 2, 4, 8 5. Find all the numbers between 95 and 130 that are: a. divisible by 3 Answer: 96, 99, 102, 105, 108, 111 b. divisible by 6 c. divisible by 9
Answer (1)
Let's go through each part of the question step-by-step:
First Three Common Multiples of 5 and 8: To find the common multiples of two numbers, list the multiples of each number and find the smallest ones they have in common.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, ...
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, ...
The first three common multiples are: 40, 80, and 120.
Common Factors of 24 and 32: To find common factors, list the factors of each number and find the ones they share.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 32: 1, 2, 4, 8, 16, 32
The common factors are: 1, 2, 4, 8.
Numbers between 95 and 130: The question asks for numbers divisible by 3, 6, and 9.
Divisible by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. The numbers between 95 and 130 divisible by 3 are: 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129.
Divisible by 6: A number is divisible by 6 if it is divisible by both 2 and 3. The numbers divisible by 6 are a subset of those divisible by 3: 96, 102, 108, 114, 120, 126.
Divisible by 9: A number is divisible by 9 if the sum of its digits is divisible by 9. The numbers between 95 and 130 divisible by 9 are: 99, 108, 117, 126.
By understanding the properties of divisibility and common factors/multiples, we can efficiently solve these types of math problems.
