Factors of 14 are the numbers that divide 14 completely without a remainder. The factors of 14 are 1, 2, 7, and 14. In this section, we will learn about the factors of 14 and the prime factors of 14.
Table of Contents
Highlights of Factors of 14
- 14=2×7 is the prime factorization of 14.
- The factors of 14 are 1, 2, 7, and 14.
- Prime factors of 14 are 2 and 7.
- Negative factors of 14 are –1, -2, -7 and –14.
Prime Factorization of 14
As 14 is an even number, it is divisible by 2. So we can write
14= 2 × 7
Here both 2 and 7 are prime numbers, so they cannot be decomposed further. Thus 14= 2 × 7 is the prime factorization of 14.
What are the Factors of 14?
Let us write the number 14 multiplicatively in all possible ways. We have:
14 = 1×14
14 = 2×7
Note that we cannot express 14 multiplicatively in any other way. So the factors of 14 in pairs are given as follows:
| 14 = a×b | Pair Factors of 14 |
| 14 = 1×14 | (1, 14) |
| 14 = 2×7 | (2, 7) |
Thus the pair factors of 14 are (1, 14) and (2, 7). As all the numbers appearing in pair factors are the factors of 14, we conclude that the factors of 14 are 1, 2, 7, and 14.
Therefore, the total number of factors of 14 is four.
| Factors of 24 : The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 |
| Factors of 20 : The factors of 20 are 1, 2, 4, 5, 10, 20 |
| Factors of 25 : The factors of 25 are 1, 5, 25 |
| Factors of 21 : The factors of 21 are 1, 3, 7, 21 |
Prime Factors of 14
Note that the factors of 14 are 1, 2, 7, and 14. Among those factors, we observe that only 2 and 7 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 14 are 2 and 7.
Question: What are the factors of 14?
Video Solution: coming soon…
How to Find Factors of 14?
Now we will determine the factors of 14 by division method. In this method, we will find the numbers that can divide 14 with no remainder. See that
| 14/1=14 and the remainder is 0 | ∴ 1 and 14 are factors of 14 |
| 14/2=7 and the remainder is 0 | ∴ 2 and 7 are factors of 14 |
Note that no numbers other than the numbers in violet color can divide 14. So the numbers in violet color, that is, 1, 2, 7, and 14 are the complete list of factors of 14.
FAQs on Factors of 14
Ans: The factors of 14 are 1, 2, 7, and 14. These are the positive factors of 14. The negative factors of 14 are -1, -2, -7, and -14.
Ans: The sum of the factors of 14 is 1+2+7+14 = 24.
Ans: No, 5 is not a factor of 14 as 14/5 is not an integer.
Ans: The prime factorisation of 14 is 14 = 2×7.
Ans: The greatest common factor of 10 and 14 is 2.
This article is written by Dr. T, an expert in Mathematics (PhD). On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.