Factors of 65 Using Prime Factorization
What are the Factors of 65?
The numbers that divide 65 completely, that is, without any remainder, are known as the factors of 65.
The factors of 65 are 1, 5, 13 and 65.
Factors of a number completely divide it. As a result, they cannot be fractions or decimals. Prime factorization will be used as a method to find the factors of 65.
Factors of 65
Hence, we now understand that the factors of 65 are numbers that divide 65 without leaving any remainder.
For example: Dividing 65 by 5 yields a quotient of 13 and a remainder of 0, which means that it is a factor of 65. The quotient, 13, is also a factor of 65.
Divide a number by 65 to see if it is a factor of 65. If the remainder is zero, the number is a factor of 65.
Prime Factors of 65
The number 65 is a composite number, that is, it has more than two numbers as factors. To carry out the prime factorization of 65, we will keep dividing 65 by its prime factors, until we get 1 as the result.
- The first step is to divide 65 by the smallest prime factor, which is 5, in this case.
65 ÷ 5 = 13
13 ÷ 13 = 1
- The prime factorization of 65 is 5 × 13, where 5 and 13 are prime numbers.
Hence, the factor tree of 65 can be written as:
Factor Pairs of 65
When a pair of factors of 65 are multiplied together to get 65 as the result, they are said to be factor pairs of 65. The examples of the factor pairs of 65 are:
- 1 × 65 = 65, (1, 65) is a pair factor of 65.
- 5 × 13 = 65, (5, 13) is a pair factor of 65.
Hence, the positive pair factors are (1, 65) and (5, 13).
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Rapid Recall
The factors of 65 are:
Solved Factors of 65 Examples
Example 1: Find the number of common factors of 36 and 65.
Solution:
The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36.
The factors of 65: 1, 5, 13 and 65.
So, the common factor of 36 and 65 is 1.
Hence, 36 and 65 have 1 as the common factor.
Example 2: Tom has a collection of 65 toy vehicles. The toy vehicles need to be arranged evenly on 5 shelves. How many toys will he place on each shelf?
Solution:
65 toy cars are to be evenly arranged on 5 shelves.
To find the number of toy cars that can be placed on each shelf, we will divide 65 by 5, that is, \(\frac{65}{5}\)
= \(\frac{5\times13}{5}\) [(5, 13) is a factor pair of 65]
= 13 [Divide both the numerator and the denominator by 65]
Hence, Tom can place 13 toy vehicles on each shelf.
Example 3: Is 3 a factor of 65?
Solution:
No, 3 is not a factor of 65 as the number 3 does not divide 65 exactly. It leaves 2 as the remainder. So, 3 is not a factor of 65.
The factors of 18 are 1, 2, 3, 6, 9, and 18 and
The factors of 65 are 1, 5, 13 and 65.
So, the common factor of 18 and 65 is 1.
The factors of 65 are 1, 5, 13 and 65.
Sum of the factors = 1 + 5 + 13 + 65
= 84
So, the sum of the factors of 65 is 84.
Yes, because 65 is made up of more than two factors, which are 1, 5, 13 and 65. In other words, just because 65 has more than two factors, it is a composite number.
The factors of 65 are 1, 5, 13 and 65.
So, the smallest factor of 65 is 1, and the greatest factor is 65 itself.
The following are some important properties of factors:
- An exact divisor of a number is called a factor.
- Every number has the number ‘1’ as its factor.
- The greatest factor of a number is the number itself.
- A factor can never be greater than the number.