Explain why a multiple of 80 is also a multiple of 8.
8*10 = 80
8*1 = 8
A multiple of 80 means that a number can be evenly divided by 80 without leaving any remainder. To understand why a multiple of 80 is also a multiple of 8, we need to understand the relationship between these two numbers.
Let's start by considering the factors of 80. Factors are the numbers that can be multiplied together to get a certain number. In the case of 80, its factors are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
Now, let's focus on the factors of 8. The factors of 8 are 1, 2, 4, and 8.
When we compare the factors of 80 and 8, we can see that they have some common factors, namely 1, 2, and 4. This means that any number that is divisible by 80 is also divisible by 1, 2, and 4.
Since a number that is divisible by 8 must be divisible by 1, 2, 4, and 8, and a multiple of 80 is divisible by 1, 2, and 4, it follows that a multiple of 80 is also divisible by 8.
Therefore, every multiple of 80 is also a multiple of 8 because they share common factors.
To understand why a multiple of 80 is also a multiple of 8, we need to first understand the concept of multiples.
A multiple is a number obtained by multiplying a given number by any integer. For example, the multiples of 8 include 8, 16, 24, 32, and so on.
Now, let's consider the number 80. We can write it as 8 multiplied by 10 (80 = 8 * 10). This means that 80 is a multiple of 8 because it can be obtained by multiplying 8 by an integer.
Since any multiple of 80 can be expressed as 80 multiplied by another integer, let's say n (where n is any integer), the general form would be 80 * n.
Now, let's express 80 * n in terms of its factors. Using the distributive property, we can rewrite it as (8 * 10) * n.
Further simplifying it, we get (8 * n) * 10.
Here we can observe that (8 * n) is an integer because n is an integer. Therefore, (8 * n) is a multiple of 8.
Now, multiplying (8 * n) by 10, we get (8 * n * 10).
Since (8 * n) is a multiple of 8 and we are multiplying it by 10 (which is an integer), (8 * n * 10) is also a multiple of 8.
Hence, any multiple of 80 is also a multiple of 8.