Factors of 39 are the list of positive and negative whole numbers that can be divided evenly into 39. There are a total of 4 factors of 39. Did you know, 39 people signed the United States Constitution and North Dakota was the 39th state to be admitted to the Union? In this lesson, we will learn to calculate the factors of 39, its prime factors, and its factors in pairs along with solved examples for a better understanding.
The number 39 is an odd composite number. As it is odd, it will not have 2 or any multiples of 2 as its factor. To understand why it is composite, let's recall the definition of a composite number. A number is said to be composite if it has more than two factors.
Consider the number 11. It has only two factors 1 and 11. Now, let's take an example of the number 60. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 There are more than two factors of 60. Thus, 60 is a composite number whereas 11 is not.
Coming back to 39, the factors of 39 are all the integers that 39 can be divided into.
How to Calculate the Factors of 39?
Let's begin calculating the factors of 39, starting with the smallest whole number, i.e., 1
Divide 39 with this number. Is the remainder 0? Yes! So, we will get, 39/1 = 39.
The next whole number is 2
Now divide 39 with this number. Is the remainder 0? No, it is not.
As already discussed in the earlier section, even numbers cannot divide 39. Hence, we need to check odd numbers only.
39/3 = 13
3 × 13 = 39
Hence, the factors of 39 are 1, 3, 9, and 13. Explore factors using illustrations and interactive examples:
Prime factorization means to express a composite number as the product of its prime factors. To get the prime factorization of 39, we divide it by its smallest prime factor which is 3.
39/3 = 13
Since 13 is a prime number, it is divisible by 13 only. This process goes on till we get the quotient as 1 The prime factorization of 39 is shown below:
Factors of 39 in Pairs
The pair of numbers which gives 39 when multiplied is known as factor pairs of 39. The following are the factors of 39 in pairs.
If we consider negative integers, both the numbers in the pair factors will be negative. 39 is a positive number and we know that the product of two negative numbers is a positive number.
Therefore, we can have factor pairs of 39 as (-1,-39) ; (-3,-13).
As 39 is an odd number, all its factors will be odd.
39 is a non-perfect square number. Thus, it will have an even number of factors. This property holds true for every non-perfect square number.
Factors are never fractions or decimals.
Ms. Evans has 39 packs of crayons. There are 3 groups of students in her class. She plans to give the packs to the three groups for an activity so that they are evenly distributed.How many packs will each group get?
Determine the following:
Factors of 35
Factors of 18
Factors of 49
Example 1: James has 39 units of a cutlery set. He wants to pack it in cartons such that these units are evenly distributed. There are two sizes of cartons available. The first size has a capacity of 9 units and the second size has a capacity of 13 units.
Which type of carton will he choose so that there is no unit left and maximum units are filled in the cartons?
How many cartons will be used?
The condition that there is no unit left means that 39 should be divided by one of those two numbers, that is, 9 or 13, and the remainder must be 0
That means the number must be a factor of 39, out of the two given numbers, 13 is a factor of 39
Thus, he will choose cartons of the second size of the capacity of 13 units.
To find the number of cartons of the second size used, we need to divide 39 by 13 i.e. 39/13 = 3.
Hence, the answers are,
The second type of carton of capacity 13 units is used
3 cartons are needed
Example 2: Jonathan's teacher gave him 2 numbers, 39 and 20, and asked him to find the common factors for both of them. Help him find common factors.
The factors of 39 are 1, 3, 13, and 39 and the factors of 20 are 1, 2, 4, 5, 10, and 20
Hence, the only common factor among the factors of 39 and 20 is 1.