When we state that a number X is a factor of a number Y, it means that Y can exactly divide X and leave no remainder. Also, when Y and Y’ multiplied gives X, then it is said that Y and Y’ are both factors of X. For example, 3 × 5 is a factorization of the integer 15 and (3,5) are factors of 15.
On that note, let’s learn how to find factors of a number by taking an example of two numbers i.e., 15 and 32 and finding their factors through different methods.
Factors of 15
We will be learning about finding factors of 15 as the product of factor pairs and prime numbers.
Factor Pairs of 15
If we consider the factors of 15 as pairs, then 15 is the result of multiplying two numbers. For instance, the answer to 1×15 is 15. In this case, the factors of 15 are considered to be the numbers 1 and 15.
In this context, the only integers that result from listing all the factors of 15 are 1, 3, 5, and 15. As 1 × 15 = 15 and 3 × 5 = 15. Because of this, only the four aforementioned numbers are referred to as factors of 15, since 15 is a product of prime numbers.
Prime Factorisation of 15
In addition to having 1 as its divisor, the integer 15 has various lower integers. As a result, 15 is known as a composite number. We shall discover the factors of 15 using the Prime Factorization method, as shown below.
The smallest prime factor known is 2. So, we’ll divide this number by 15 (15 ÷ 2 = 7.5). Since the result is a decimal on (7.5), 2 is not considered a prime factor of 15.
Let’s go on to the next number, which is 3 (15 ÷ 3 = 5). Again, dividing 5 by 3 yields 5 ÷ 3 = 1.67, which is also a fractional result (1.67).
Let us now divide 5 by the next prime integer, which is 5 (5 ÷ 5 = 1). We’re not going any further with the number division because we received outcome 1.
As a result, we understand the numbers 5 and 3 as prime factors of 15, where both 3 and 5 are prime numbers.
Factors of 32
The integers that can be divided equally into 32 are known as factors of 32. There are six factors of 32: 1, 2, 4, 8, 16, and 32. The sum of all 32 factors is 63. It has Factors 1, 2, 4, 8, 16, 32, and Pair Factors (1, 32), (2, 16), (3, 32), (3, 32) and (4, 8).
What are Factors of 32?
- A factor is a number that precisely divides another number, leaving no remainder.
- The number 32 is an even composite number. If a number contains more than two factors, it is said to be composite.
- Think about the number 23. It only has two factors, 1 and 23. It is prime because it is only divided by one and 23. Think about the number 48. It has more than two factors, making it a composite number.
Factors of 32 are integers that divide 32 without leaving a remainder, and they are 1, 2, 4, 8, 16, and 32.
How to Calculate Factors of 32?
- Let us begin with the whole number 1 and work through the factors of 32.
32 ÷ 1= 32
- Then, divide the quotient (32) by 2.
32 ÷ 2= 16
- Next, we get.
32 ÷ 4= 8
- Similarly, we complete the calculation of all 32 factors, which are 1, 2, 4, 8, 16, and 32.
