Certainly! Let's break down and answer each part of the question step-by-step.
### Step 1: Explanation of "Every factor is a factor of"
A factor of a number is a whole number that divides the given number exactly with no remainder. For example, factors of 10 are 1, 2, 5, and 10.
### Step 2: The number of factors of a given number
The number of factors of a given number can be determined by evaluating the number's prime factorization. For instance, let's take the number 12:
- The prime factorization of 12 is [tex]\(2^2 \times 3^1\)[/tex].
To find the total number of factors:
1. Increase each of the exponents in the prime factorization by one.
- For 12: [tex]\((2+1)(1+1) = 3 \times 2 = 6\)[/tex].
So, the number 12 has six factors: 1, 2, 3, 4, 6, and 12.
### Step 3: The number of multiples of a given number
A multiple of a number is that number multiplied by an integer. For example, multiples of 5 are 5, 10, 15, 20, etc.
### Step 4: 121 as a factor of every number
121 is not a factor of every number. A number must exactly divide into another to be considered its factor. Since 121 is [tex]\(11^2\)[/tex], it is only a factor of numbers that can be divided by 121, not every number.
### Step 5: Every multiple of a number is [tex]$\qquad$[/tex] or equal to the number
Every multiple of a number is greater than or equal to the number.
- For example, multiples of 7: 7, 14, 21, 28, etc.
- Each of these multiples is greater than or equal to 7.
By detailing each step, we can now fully understand the relationships and properties between factors and multiples of numbers.
