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When you multiply any two numbers, it doesn’t matter whether it is a single digit or double digit, you must get the result as 28. Now these numbers will be known as the factors of 28. It can be divided evenly by a set of numbers called its factors. In total, there are 6. The largest factor of this number is itself, and the other positive factors are 1, 2, 4, 7, and 14. The sum of all these factors is 56.
Table of Contents
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Definition and Properties
A factor of a number is a positive whole number (no decimals or fractions) that divides evenly into another number (leaving no remainder). You can check for factors by dividing the larger number by the potential factor; if there’s no remainder, it’s a factor. Remember, since dividing by zero is undefined, zero cannot be a factor of any number.
When we break down a number into its prime factors, we are essentially breaking it down into the building blocks that multiply together to get that number.
Below are the factors:
- Factors: 1, 2, 4, 7, 14, and 28
- Negative Factors: -1, -2, -4, -7, -14 and -28
- Prime Factors: 2, 7
- Prime Factorization: 2 × 2 × 7 = 22 × 7
- The sum of Factors: 56
1, 2, 4, 7, 14, and 28 are the factors of the given number.
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Prime Factorization Method of Factors of 28
The prime factorization of 28 is simply 2 (2 multiplied by itself three times). We can also group factors into pairs. Factors come in pairs because when you multiply them together you get the original number. So, for example, 1 and 28 are a pair of factors of 28 because 1 x 28 = 28. The other pairs of factors of the number are (2, 14) and (4, 7).
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Using the factorization approach, a number is broken down into its smaller, simpler parts, or factors. Real and rational numbers, as well as division, must be understood. We can determine the factors of 28 by using this.
Break down the number by its smallest prime factor: The smallest prime number that divides 28 evenly is 2. We can write this as:
28 = 2 * 14
Continue breaking down the remaining factor: Since 14 is not a prime number, we can try to divide it by 2 again. We get:
28 = 2 * (2 * 7)
Identify the prime factors: We’ve reached prime factors because 2 and 7 are both prime numbers (they cannot be further divided into whole numbers). Therefore, the prime factorization of 28 is:
28 = 2 x 2 x 7
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