What is a Factor | How To Factor a number?

When learning about factors in Math. We come across questions like what is a factor? how to factor a number? How to find the factors of a number? Factor is one of the most important topics often introduced in grade 5 or 6 in Mathematics. Let’s understand more about this topic “factors“.

Definition of Factors with Example

Think of these factors as the building blocks of numbers. Factors, in simple terms, refer to positive numbers that can be divided evenly into another number. In other words, factoring a number is the different integers that can be multiplied together to give us that number. These integers are like the ingredients in a recipe, and when combined in just the right way, they whip up the number we’re trying to understand.

For Example, Let’s take the number as 10. Its factors are 1, 2, 5 and 10. Why? Because 1 x 10 = 10, 2 x 5 = 10, and so on. These are the numbers that fit perfectly into the puzzle of 10.

Let’s take another example, Consider the number 16

The factors of 16 are the numbers that can be multiplied together to give the product 16. So, let us understand the logic of calculating the factor of number 16.

1, 2, 4, 8, and 16.

These numbers can be multiplied in various combinations to result in 16:

1 * 16 = 16
2 * 8 = 16
4 * 4 = 16

So, the factors of 16 are 1, 2, 4, 8, and 16.

How to find factors of numbers?

Let’s understand the ways to find factors of numbers. In mathematics, we have prime numbers and composite numbers. So, a prime number of factors are 1 and itself. It cannot be further factorized. When we multiply another whole number with a prime number it’s called a composite number.

factor of prime numbers

factor of composite numbers

Properties of Factors

1. For all the number 1 is the common factor.
2. For 1, the factor would be 1.
3. All the numbers have finite factors and will be equal to or less than the given number.
4. We can calculate factors using multiplication and division methods.

What is a factor for Prime numbers and composite numbers?

Prime Numbers in mathematics are the whole numbers that are greater than 1 and whose factors are 1 and the number itself. A few of the prime numbers are 2,3,5,7 and so on.

For example, Find the prime factors of 2 & 5

Solution: The Prime factor of 2 is 1,2. And the prime factor of 5 is 1,5.

Likewise, we have composite numbers is a natural or positive integer integer which has more than 2 factors.

How to find the prime factorization of a composite number?

One of the most important question arise over here “What is Prime factorization ?“In prime factorization, a composite number is decomposed into its prime factors, i.e., the prime numbers that divide the composite number evenly.

Let’s understand this with a step-by-step process by factorizing “n” :

• Start with the smallest prime number: Start by dividing the composite number “n” by the smallest prime number, which is 2, and continue dividing by 2 until it is no longer divisible by 2.
• Go for the next Prime number: Move on to the next prime number, which is 3. Divide “n” by 3 repeatedly until it’s no longer divisible by 3
• Continue dividing with Prime Numbers: Continue this process with successive prime numbers (5, 7, 11, …) until you’ve tested all primes less than or equal to the square root of the remaining value of “n”.
• Remaining Value: After dividing by all the primes, the remaining value of “n” is either 1 or a prime number. If it’s 1, you have found all the prime factors. If it’s a prime number, this prime is also one of the factors.
• Collect the Factors: Collect all the prime factors you found in the previous steps. They are listed in ascending order.

Example to Understand Prime Factorization

For example: Let’s find out the prime factorization of 56

1. Dividing 56 by 2 gives 28.
2. Dividing 28 by 2 gives 14.
3. Dividing 14 by 2 gives 7.
4. Since 7 is a prime number, the prime factorization of 56 is 2 x 2 x 2 x 7, or simply 2^3 x 7.

Keep in mind that when we’re dealing with bigger composite numbers, the prime factorization can get a bit trickier. But the process remains the same: divide by primes until you can’t divide anymore, and collect the prime factors obtained.

But here’s the cool part – prime factorization isn’t just about breaking down numbers. It’s like a secret tool that helps you find other hidden treasures in the world of numbers. For instance, you can also use prime factorization to discover the greatest common divisor (GCD) and the least common multiple (LCM) of two or more numbers. It’s like getting extra mileage out of your prime factorization skills.

How To Find Factors of a Number?

Mathematics always has different approaches to solving any problem. In the topic “What is a factor ? & How To Factor a number?”. We will deal with two ways to find the factor of any number in mathematics. The two methods which we will discuss here are division and multiplication.

First Method: Finding factors of a number using the Division Method

Let’s find the factors of 10

Always remember that factors come in pairs: if a number “a” is a factor of “b,” then “b ÷ a” is also a factor of “b.” In the example above, 2 is a factor of 10, and 10 ÷ 2 = 5, which is also a factor of 10.

So, the factors of 10 would be 1,2,5,10

This process works for any positive integer. Just follow these steps, and you’ll be able to find the factors of a number.

Second Method: Finding factors of a number using the Multiplication method

Let’s find out the factors using the Multiplication method.

So, as we discussed earlier. The factors come in pairs. Here, the pair would be (1,10) &(2,5). As a result, the factors of 10 would be 1,2,5,10.

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