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Factors of 21

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Introduction to Factors of 21

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Wondering what are the factors of 21? Factors of 21 are actually all the integers that mean the entire positive, negative and whole numbers that we can divide into 21 evenly. What’s amazing is that 21 divided by a factor of 21 will be equivalent to another factor of 21. These can be thus expressed as either individual factors or as paired factors. In such a situation, we showcase them both ways. This is typically a mathematical dissolution of a specific number.


Finding the Factors of 21

Seeing that the factors of 21 are all the numbers that we are able to evenly divide into 21, we simply require dividing 21 by all numbers up to 21 to observe which ones conclude to an even quotient. When we do this, we will observe that these computations resulted in an even quotient like these below:

21/21 = 1

21/7 = 3

21/3 = 7

21/1 = 21


Positive Factors of 21

The positive factors of 21 are all the numbers we can divide (divisors) to obtain an even number.


Prime Factorization of 21

A prime factorization is an outcome of factoring a number into classification of components in which every member is a prime number. This is usually expressed in written form by presenting 21 as a product of its prime factors. For 21, this outcome will be: 21 = 3 x 7. Therefore, the total number of prime factors of 21 is 2.


Is 21 a Square Number or Not?

No! Number 21 is not considered a square number in mathematics. The square root of this number is 4.58 which is not an integer.


Is 21 a Composite Number or Not?

Yes! 21 is a composite number. The number 21 is actually the product of two positive numbers other than 1 and itself which makes it a composite number. In other words, because 21 can be divided by one, itself and by 3 and 7, thus it is a composite number. A composite number is an integer that is divided by at least another natural number, apart from itself and 1, without leaving a remainder.


Total Number of Factors of 21

Factors of 21 have 4 positive factors and 4 negative factors. Hence, the total number of Factors of 21 is 8.

Number 21 has 4 positive factors in total i.e.: 1, 3, 7 and 21

Number 21 has 4 negative factors in total i.e.: -1, -3, -7 and -21

More particularly, presented as pairs...

[1 × 21] [3 × 7] [7 × 3] [21 × 1]


Highest Common Factor of 21 And Another Number

The highest common factor (HCF) of two numbers can be identified by setting a comparison between prime factorization of the two numbers and taking off the highest common prime factor. If there does not exist any common factor, the HCF is 1. This is also called the greatest common factor and is a crucial component of the common prime factors of two numbers. It is the largest factor or we can say the largest number the two numbers share as a prime factor.


Least Common Factor of 21

The least common factor or we shall say the smallest number in common of any pair of integers is 1.


Finding The Least Common Multiple of 21 And Another Number

We can simply find the least common multiple of 21 through an easy solution that rests in the lowest common multiple of two numbers. You can also use a least common multiple calculator available at Vedantu for providing utmost convenience to students learning factorization.

FAQ (Frequently Asked Questions)

1. What Do We Understand by a Factor Tree?

A factor tree is basically a graphical illustration of all the possible factors of the numbers and their sub-factors. It is mainly created in order to simplify factorization. It is designed by identifying and evaluating the factors of a number, then determining the factors of the factors of a number. The process continues in a periodic motion until you've extracted a collection of prime factors, which is the prime factorization of the original number. In building the factor tree, make sure you remember the 2nd item in a factor pair.

2. How Can We Find the Factors of  -21 or other Negative Numbers?

In order to evaluate the factors of -21 or any other negative number, we would need to find all the positive factors and then replicate them by adding a minus (-) sign before each one (multiplying them by -1). This system inscribes negative factors.

3. What Are the Divisibility Rules?

Divisibility is what we refer to a given integer which is being divisible for a given divisor. The divisibility rule is a shorthand mathematical technique to identify what is or isn't divisible. This includes rules about even number as well as odd number factors. The rule is proposed to enable the student to evaluate the status of a given number without calculation.

4. How Can We Find Factors for a Particular Number?

Simply you can use a factor calculator. If you need the factors for a specific number, you will have to simply submit a number in the calculator box in order to find the factors for that number. You will also get the detailed explanations at the online portal of Vedantu.