Factors of 21 Using Prime Factorization
What is meant by the Phrase “Factors of 21?”
The factor of 21 is a natural number that divides 21 evenly, leaving zero remainder.
1, 3, 7, and 21 are the factors of 21.
How can we find the Factors of 21?
Divisibility rules and division facts can be used to determine the factors of a number. Here is a list of the factors of 21.
We can stop checking after 6 as the factor pairs start to repeat.
Hence, the factors of 21 are 1, 3, 7, and 21.
[Note: To check whether a number is a factor of 21, divide 21 by that number and check the value of the remainder. If the remainder is zero, the number is a factor of 21, otherwise not.]
The Prime Factors of 21
Expressing a number as a product of prime numbers is known as the prime factorization of the number. Here, the prime numbers multiplied are known as the prime factors of the number. A factor tree can be used to prime factorize any number.
The factor tree below shows that the prime factorization of 21 = 3 x 7.
Hence, the prime factors of 21 are 3 and 7.
The Factor Pairs of 21
The factor pair of a number is the set of two of its factors, such that the product of the factors is the number itself. A factor pair can be a positive pair or a negative pair.
The factor pairs of any number can be obtained from the list of its factors.
For example, (3,7) is a factor pair of 21, as 3 x 7 = 21.
Hence, the factor pairs of 21 are (1,21) and (3,7).
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Rapid Recall
The factors of the number 21 are 1, 3, 7, and 21.
The positive factor pairs of 21 are (1, 21) and (3, 7).
The prime factors of the number 21 are 7 and 3.
Solved Factors of 21 Examples
Example 1: What are the common factors of 21 and 52?
Solution:
The factors of 21 are 1, 3, 7, and 21.
The factors of 52 are 1, 2, 4, 13, 26, and 52.
Hence, the common factor of 21 and 52 is 1.
Example 2: What is the greatest common factor of 21 and 99?
Solution:
The factors of 21 are 1, 3, 7, and 21.
The factors of 99 are 1, 3, 9, 11, 33, and 99.
So, the common factors of 21 and 99 are 1 and 3.
Hence, the greatest common factor of 21 and 99 is 3.
Example 3: How many common factors do 21 and 42 have?
Solution:
The factors of 21 are 1, 3, 7, and 21.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
So, the common factors of 21 and 42 are 1, 3, 7, and 21.
Hence, 21 and 42 have a total of 4 common factors.
Example 4: 21 chocolates were neatly placed in a box. If there were 7 rows of chocolates, how many chocolates were placed in each row?
Solution:
We know that there are a total of 21 chocolates. We also know that there are 7 rows of chocolates. To obtain 21 as the result, there is only one factor pair. The factor pair is 7 and 3.
7 x 3 = 21
Since we know that there are 7 rows, it means that each row should have 3 chocolates.
A multiple of 21 is obtained by multiplying 21 by any natural number , whereas a factor of 21 divides 21 evenly, leaving a zero remainder.
For example, 42, 63, 84, and so on are the multiples of 21 and 1, 3, 7, and 21 are the factors of 21.
The number 21 has more than two factors. So, 21 is not a prime number.
A number that has more than two factors is a composite number. Other than 1 and 21, the number 21 includes two additional factors, which are 7 and 3. Therefore, it is a composite number.
When 21 is divided by 5, the remainder is 1, that is, not zero. So, 21 is not evenly divisible by 5, and hence 5 is not a factor of 21.