Factors of 14 Using Prime Factorization
What are the Factors of 14?
The factors of 14 are natural numbers that divide 14 without leaving any remainder. In other words, the factors of 14 divide 14 evenly.
Example: 7 is a factor of 14 because when we divide 14 by 7, it gives us 2 as the quotient and 0 as the remainder. Here, the quotient 2 is also a factor of 14.
So, to check if any number is a factor of 14 or not, divide 14 by that number and verify whether the remainder is zero or not. If the remainder is zero, the number is a factor of 14, otherwise not.
Factor List of 14
The factors of 14 can be obtained by applying the divisibility rules and division facts.
You can stop checking after 2 as the factor pairs start to repeat.
So, the factors of 14 are 1, 2, 7, and 14.
The Prime Factors of 14
A factor tree can be used to learn about the prime factorization of 14.
From the factor tree, we can see that the prime factorization of 14 = 2 × 7.
This means 2 and 7 are the prime factors of 14.
The Factor Pairs of 14
The factor pair of 14 is the combination of two factors of 14, which when multiplied together result in 14.
Example: (2, 7) is the factor pair of 14 as 2 x 7 = 14.
The factor pairs of a number can be obtained from the list of factors of the number. A factor pair can be a positive pair or a negative pair.
Factor pairs of 14
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Rapid Recall
Solved Factors of 14 Examples
Example 1: Find the common factors of 14 and 7.
Solution:
The factors of 14: 1, 2, 7, and 14.
The factors of 7 : 1 and 7.
So, the common factors of 14 and 7 are 1 and 7.
Example 2: Find the greatest common factors of 14 and 21.
Solution:
The factors of 14: 1, 2, 7, and 14.
The factors of 21: 1, 3, 7, and 21.
So, the common factors of 14 and 21 are 1 and 7.
Therefore, the greatest common factor of 14 and 21 is 7.
Example 3: Find the product of all the prime factors of 14.
Solution:
The prime factors of 14 are 2 and 7.
The product of the prime factors = 2 × 7
= 14.
So, the product of all the prime factors of 14 is 14.
Example 4: A teacher wants to arrange chairs for each of the 14 students in the class. She wants to arrange the chairs in 7 columns. How many chairs will she place in each column?
Solution:
14 students will require 14 chairs in total.
So, 14 chairs are arranged in 7 columns.
To find out how many chairs are placed in each column, we will divide 14 by 7, that is,
\(\frac{14}{7}\)
= \(\frac{7 \times 2}{7}\) [(2, 7) is a factor pair of 14]
= 2 [Divide both the numerator and the denominator by 7]
As a result, 2 chairs will be placed in each column.
No, when you divide 14 by 3, it will give 2 as a remainder, that is, 3 does not divide 14 evenly.
Numbers that divide 14 evenly, that is, leave zero as the remainder, are known as the factors of 14.
The factors of 14 are 1, 2, 7, and 14.
Hence, the sum of all the factors of 14 is
= 1 + 2 + 7 + 14 = 24
Hence, the sum is 24.
Yes, 14 is a composite number as it has factors other than 1 and itself. It has the factors 2 and 7 other than 1 and 14.
The factors of 14 are 1, 2, 7, and 14.
So, the least factor of 14 is 1, and the greatest factor is 14 itself.