Definition of factors of 65: If a number completely divides 65 without leaving a remainder, then that number is called a factor of 65. Thus, we can say that the factors of 65 are the divisors of 65.
Here, we will learn about the factors of 65 and the prime factors of 65. We have:
- 65 = 5×13 is the prime factorization of 65.
- The factors of 65 are 1, 5, 13, and 65.
- The prime factors of 65 are 5 and 13.
- Negative factors of 65 are –1, -5, -13, and –65.
Table of Contents
What are the Factors of 65?
Let us write the number 65 multiplicatively in all possible ways. We definitely have:
| 65 = 1×65 |
| 65 = 5×13 |
As there are no other ways we can write 65 multiplicatively, so we will stop right now. So the factors of 65 in pairs are given as follows:
| 65 = a×b | Factors in Pairs (a,b) |
| 65 = 1×65 | (1, 65) |
| 65 = 5×13 | (5, 13) |
Thus the pair factors of 65 are (1, 65) and (5, 13). As all the numbers appearing in pair factors are the factors of 65, we conclude that
|
The factors of 65 are: 1, 5,13, and 65. |
Number of Factors of 65
From above we have calculated the factors of 65 which are 1, 5, 13, and 65.
Thus the total number of factors of 65 is four.
Prime Factors of 65
Note that the factors of 65 are 1, 5, 13, and 65. Among those factors, we observe that only 5 and 13 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 65 are 5 and 13.
Question: What are the factors of 65?
Video Solution:
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How to Find Factors of 65?
Now we will determine the factors of 65 by division method. In this method, we will try to find the numbers that can divide 65 with no remainder. See that
65/1=65 and the remainder is 0.
∴ 1 and 65 are factors of 65.
65/5=13 and the remainder is 0.
∴ 5 and 13 are factors of 65.
Note that no numbers other than the numbers in violet color can divide 65. So the numbers in violet color, that is, 1, 5, 13, and 65 are the complete list of factors of 65.
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