What is Meant by Factors?
A factor of a number is an integer that divides the number evenly, that is, leaving no remainder. The factors of a number can be determined using divisibility rules and division facts. Here, we will learn about the factors, prime factors, and factor pairs of 39.
What are the Factors of 39?
The factors of 39 are those integers that divide 39 without leaving any remainder. In other words, we can say that the factors of 39 will divide it evenly.
The factors of 39 can be positive as well as negative, but they cannot be decimals or fractions. The quotient obtained on dividing 39 by its factor is also a factor of 39.
The factors of 39
For example, 3 is a factor of 39 because when 39 is divided by 3, it leaves 0 as the remainder and 13 as the quotient, which is also a factor of 39.
Factor List for the Number 39
Divisibility rules and division facts can be used to determine the factors of 39.
If we continue the same way, we will notice that the number will repeat on reaching 13. Hence, we can stop checking the factor pairs after 12 as they begin to repeat.
The factors of 39 are 1, 3, 13, and 39
The Prime Factors of 39
A factor tree can be used to determine the prime factors of 39, as shown in the figure.
From the factor tree, we can see that the prime factorization of 39 is 3 x 13.
This means 3 and 13 are the prime factors of 39.
The Factor Pairs of 39
The factor pair of any number is a set of two integers that, when multiplied, result in that number itself. So, the two integers are the factors of the number. A factor pair can be negative or positive.
[Note: The product of two negative numbers is positive.]
The factor pair of 39 is the set of two factors of 39 that, when multiplied, give 39 as the product.
Thus, the factor pairs of 39 can be obtained from the list of its factors.
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Rapid Recall
Solved Factors of 39 Examples
Example 1: A school library has a collection of 39 books on the geography of America. The books are to be arranged evenly on 3 shelves. How many books will be placed on each shelf?
Solution:
39 books are to be evenly arranged on 3 shelves.
To find out how many books can be placed on each shelf, we will divide 39 by 3, that is,
\(\frac{39}{3}\)
= \(\frac{13~\times~3}{3}\) [(3, 13) is a factor pair of 39]
= 13 [Divide both the numerator and the denominator by 3]
As a result, 13 books can be placed on one shelf.
Example 2: Find the common factors of 175 and 39.
Solution:
Factors of 175: 1, 5, 7, 25, 35, 175
Factors of 39: 1, 3, 13, 39
So, the common factor of 39 and 135 is 1.
Hence, 135 and 39 have only one common factor.
Example 3: What are the common factors of 39 and 168?
Solution:
The factors of 39 are 1, 3, 13, 39
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
So, the common factors of 39 and 168 are 1 and 3.
Yes, 3 is a factor of 39. This is because the number 3 divides 39 exactly, that is, it leaves 0 as the remainder. So, 3 is a factor of 39.
Yes, 39 is a composite number as it has factors other than 1 and itself, that is, 39. In other words, the number 39 has more than two factors.
The factors of 39 are 1, 3, 13, 39
So, the smallest factor of 39 is 1, and the greatest factor is 39 itself.
The factors of 39 are 1, 3, 13, 39
Hence, the sum of the all the factors of 39 is
= 1 + 3 + 13 + 39 = 56
Hence, the sum is 56.
The factors of 39 are 1, 3, 13, 39. So, 39 has 4 factors.