Factors of 7 Using Prime Factorization
Factors of 7
Factors | Factors pairs | Prime factorization |
|---|---|---|
1, 7 | (1, 7) | \(7~=~7~\times~1 \) |
What are the Factors of 7
Factors of 7 are integers that divide 7 without leaving any remainder, or in other words, factors of 7 divide 7 exactly.
Example: 7 is a factor of 7 because when we divide 7 by 7, it gives us the quotient as 1 and the remainder as 0. The quotient, 1, is also a factor of 7.
So, to check if any number is a factor of 7, we divide 7 by that number and check if the remainder is zero or not.
Factor List of 7
Factors of 7 can be obtained as follows:
Hence, the factors of 7 are 1 and 7.
Prime Factorization of 7
A factor tree can be used to learn about the prime factorization of 7.
The factor tree of 7 can be written as:
From the factor tree we can see that the prime factorization of 7 is 1 × 7 = 7.
This means that 7 is a prime number as it has no other factors other than 1 and itself.
Factor Pairs of 7
The factor pair of 7 is the set of two factors of 7 which when multiplied together result in 7.
Example: (1, 7) is a factor pair of 7, because 1 and 7 are factors of 7 and \(1~\times~7~=~7 \)
Positive Factor Pairs of 7
Read More:
Rapid Recall
Solved Factors of 7 Examples
Example 1: Find the common factors of 14 and 7.
Solution:
Factors of 14: 1, 2, 7 and 14.
Factors of 7: 1 and 7.
So, the common factors of 14 and 7 are 1 and 7.
Example 2: How many factors does 7 have?
Solution:
Factors of 7: 1 and 7.
So, there are 2 factors of 7.
Example 3: Find the product of all the prime factors of 7.
Solution:
Prime factors of 7 are 1 and 7.
Product of prime factors = 1 × 7
= 7.
So, the product of all the prime factors of 7 is 7.
Example 4:
Miranda finished all seven of her comic books. Now, she intends to share her books equally with her three friends. If any books are left behind, she would donate them to the local library. Will she end up donating any?
Solution:
Number of books = 7
Number of friends = 3
\(\frac{7}{3} \) = 2 R1
On dividing 7 by 3, we get the quotient as 2 and the remainder as 1. So, Miranda can give 2 books each to three of her friends. After distributing among her friends, she would be left with 1 book.
Therefore, Miranda can donate 1 book to the local library.
No, when you divide 7 by 3, we will get 1 as a remainder, that is, 3 does not divide 7 exactly.
Numbers that divide 7 exactly, that is, leave zero as the remainder are known as the factors of 7.
The factors of 7 are 1 and 7.
Hence, the sum of all the factors of 7 is 1 + 7 = 8
Hence, the sum is 8.
The factors of 7 are 1 and 7 itself. It does not have any other factors. Hence, 7 is a prime number and not a composite number.
The factors of 7 are 1 and 7.
So, the least factor of 7 is 1, and the greatest factor of 7 is 7 itself.