You can find out what a number is divided by in a few different ways, depending on what you're trying to accomplish. Here's a breakdown:
1. Knowing the Divisor
If you know what number you want to divide by (the divisor), then you're essentially performing a division operation. For example, if you want to find out what 20 is divided by when divided by 5, you perform the division: 20 / 5 = 4. The answer, 4, is called the quotient.
2. Finding Factors (Divisors) of a Number
If you want to find all the numbers that divide evenly into a given number, you're looking for the factors or divisors of that number. This involves systematically checking numbers to see if they divide evenly (i.e., result in a whole number).
Example: Finding the factors of 12
- 1 divides 12 (12 / 1 = 12)
- 2 divides 12 (12 / 2 = 6)
- 3 divides 12 (12 / 3 = 4)
- 4 divides 12 (12 / 4 = 3)
- 6 divides 12 (12 / 6 = 2)
- 12 divides 12 (12 / 12 = 1)
Therefore, the factors (divisors) of 12 are 1, 2, 3, 4, 6, and 12.
3. Using Divisibility Rules
Divisibility rules are helpful shortcuts to quickly determine if a number is divisible by another number without performing long division. Here are a few common rules:
- Divisible by 2: The number ends in an even number (0, 2, 4, 6, 8).
- Divisible by 3: The sum of the digits is divisible by 3.
- Divisible by 5: The number ends in 0 or 5.
- Divisible by 10: The number ends in 0.
Example: Is 123 divisible by 3?
1 + 2 + 3 = 6. Since 6 is divisible by 3, then 123 is also divisible by 3.
4. Prime Factorization
Finding the prime factorization of a number can help you determine all of its divisors. Prime factorization is expressing a number as a product of its prime factors (numbers only divisible by 1 and themselves).
Example: Prime factorization of 24
24 = 2 x 2 x 2 x 3 = 23 x 3
From the prime factorization, you can systematically create all possible combinations of these prime factors to find all the divisors of 24 (1, 2, 3, 4, 6, 8, 12, 24).
Summary
Finding out what a number is divided by depends on whether you already know the divisor or if you are trying to find the divisors (factors) of a number. Knowing divisibility rules, understanding prime factorization, and systematically testing numbers can help you determine what a number is divisible by.
