Definition of factors of 7: If a number completely divides 7 with the remainder zero, then that number is called a factor of 7.
By the above definition, we can say that the factors of 7 are the divisors of 7. In this section, we will learn about the factors of 7 and the prime factors of 7.
Also Read: Basic concepts of factors
Highlights of Factors of 7
- 7=1×7 is the prime factorization of 7.
- The factors of 7 are 1 and 7.
- The only prime factor of 7 is 7.
- Negative factors of 7 are –1 and –7.
What are the factors of 7?
To get the factors of 7 we need to first write the number 7 multiplicatively in all possible ways.
7 = 1×7
This is the only way we can express 7 multiplicatively. Therefore the factors of 7 in pairs are given as follows:
|7 = a×b||Factors in Pairs (a,b)|
|7 = 1×7||(1, 7)|
Thus the only pair factor of 7 is (1, 7). We know that all the numbers appearing in pair factors are the factors of 7. So we conclude that
The factors of 7 are:
1 and 7.
Number of factors of 7
From above we have calculated the factors of 7 which are 1 and 7. Thus the total number of factors of 7 is two.
Prime Factors of 7
Note that the factors of 7 are 1 and 7. Among those factors, we observe that only 7 is a prime number as it does not have any proper divisors.
∴ the only prime factor of 7 is the number 7 itself.
Question: What are the factors of 7?
Video Solution: coming soon…
Is 7 a Prime Number?
As the factors of 7 are 1 and the number itself, by the definition of prime numbers, we can say that 7 is a prime number.
Conclusion: 7 is a prime number.
How to find factors of 7?
Now we will determine the factors of 7 by division method. In this method, we will find the numbers that can divide 7 with no remainder. We have:
|7/1=7 and the remainder is 0.||∴ 1 and 7 are factors of 7.|
Note that no numbers other than the numbers in violet color can divide 7. So the numbers in violet color, that is, 1 and 7 are the complete list of factors of 7.