Factors of 5 | Prime Factorization of 5 | Factor Tree of 5

Factors of 5

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What are the factors of 5

The factors of the number 5 are the numbers that can divide the number 5 entirely with zero remainders and no decimal points in the quotient. And so the factors of 5 are 1 and 5.
To find the factors of a number, you can divide the number by each of the numbers that are smaller than it, starting from 1. If the result of the division is an integer (no remainder), then that number is a factor of the original number. For example, let’s find the factors of 5 by the following steps:
First, let’s divide 5 by 1. The result is 5, which is an integer. So, 1 is a factor of 5.
Now, divide 5 by 2. The result is 2.5, which is not an integer. So, 2 is not a factor of 5.
Now, let’s divide 5 by 3. The result is 1.66, which is not an integer. So, 3 is not a factor of 5.
Divide 5 by 4. The result is 1.25, which is not an integer. So, 4 is not a factor of 5.
Therefore, the only numbers that divide evenly into 5 are 1 and 5, those numbers are the only factors of 5.

How to find factors of 5?

• Factors of 5 using the Multiplication Method
• Factors of 5 using the Division Method
• Prime Factorization of 5
• Factor tree of 5

Factors of 5 Using the Multiplication Method

• The factors of a number can be determined using the multiplication method:
• First of all, write down the number for which you want to find the factors. Here, in this case, it’s 5.
• Now, write down the factors of the number 5 which are so far familiar to you. For now, let’s take 1 and 5 as the factors of 5, as for every given number 1 and the given number will always be its factors.
• Now check if any other number that you have written down can be multiplied together to get the original number 5. In this case, 1 x 5 = 5, which means that 1 and 5 are the factors of 5.
• And now, if you are unable to find any more factors using this method, then this indicated that you have found all the factors of 5. Therefore, in this case, 1 and 5 are the only factors of the number 5. When they are multiplied together the result is the number 5.
• In short, the factors of the number 5 are 1 and 5 using the multiplication method.

Factors of 5 using Division Method

• To find the factors of a number using the division method are as follows:
• First of all, write down the number whose factors you want to find. In this case, let’s take the number 5.
• Now let’s start dividing the given number 5 by 1. If the resulting value is an integer, then 1 is definitely the factor of 5.
• If the result of the division is not an integer, then try dividing it with the next number, which is 2. In this case also if the resultant is not an integer, then move on to divide the number 5 by the next number.
• Do continue this process, until you have tried dividing the given number 5 by all the numbers that are smaller than it. Here, this method can be applied to 3 and 4 as they are smaller than 5.
• And so finally the numbers that have resulted in an integer when divided it by the given number are the factors of that given number. Here, the only number that resulted in an integer was 1 and so, 1 is the only factor of 5 along with the number 5 itself.

Prime Factorization of 5

• The prime factorization of the given number 5 is 5.
• To find the prime factorization of a number, first you need to find the prime numbers that when multiplied together produce the given number. For, example, let’s take the number 5 itself. The prime factorization of the number 5 is 5 itself. As the number 5 is a prime number and it cannot be factored further into any other prime numbers.
• The prime factorization of a number is written as the product of its prime factors. For example, the prime factorization of 5 is written as 5.

Factor Tree of 5

A factor tree is a diagrammatic way to represent the prime factorization of a composite number (The numbers that have more than two factors). In this method, the given number is broken down into smaller factors till the branches in the factor tree get prime numbers. Here is the factor tree of 5:

In this case, the prime factorization of 5 is 5 itself, as 5 is a prime number.
In order to create the factor tree for a composite number, you would start finding two factors of the number that are prime numbers. For example, the factor tree of 20 would be:
2 x 2 x 5, and this will be represented in the factor tree.

Factor Pairs of 5

The factor pairs of a number are all those combinations of numbers which when multiplied together result in the given number. For example, in this case, the factor pairs of 5 are (1, 5) and (5, 1), as 1 x 5 = 5, and 5 x 1 = 5.
In general, the factor pairs of a number can be found by listing all the factors of the given number and then pairing them in all possible combinations. For example, the factors of 5 are 1, 5, and therefore, the pair factors of 5 are (1, 5), (5, 1).
It’s very important to know that the order of the factors in a factor pair doesn’t matter, as the multiplication process is commutative (Which means, that the order of the numbers being multiplied doesn’t change the result). This means that (1, 5) and (5, 1) are considered the same factor pair.

More Factors

• Factors of 2
• Factors of 3
• Factors of 4
• Factors of 5
• Factors of 6
• Factors of 7
• Factors of 8

Factors of 5- Quick Recap

• Negative Factors of 5: -1, -5
• Prime Factors of 5: 5
• Prime Factorization of 5: 1, 5

Solved Examples of Factors of 5

Q.1: What is the product of two even numbers whose sum is also equal to five?
Solutions: There are no two even numbers whose sum is equal to five. Even numbers are divisible by 2 and their sum will always be an even number.

Q.2: Jane needs to divide a number by 5, but her answer must be a whole number; which number could she use?
Solutions: Any multiple of 5 will satisfy this condition. In general, any number that can be expressed as 5 multiplied by another whole number will yield a whole number when divided by 5.

Q.3: How many pairs of factors are needed to multiply together in order to equal twenty-five?
Solutions: Two pairs of factors are needed to multiply together in order to equal twenty-five; these would include 5×5=25 and 1×25 = 25.

Q.4: Find three prime numbers multiplied together and generate a product that is divisible by five.
Solutions: Here’s an example of three prime numbers multiplied together to generate a product that is divisible by five: 2 × 3 × 5 = 30

Q.5: Danny needs to reduce an equation by half but keep it divisible by five; what equation could he use?
Solutions: Original equation: 10x = 50. If Danny reduces this equation by half, he would have 5x = 25. In this case, the equation is divisible by 5 (5x) and the result (25) is also divisible by 5.

Q.6: How many factors does twenty have where none exceeds seven?
Solutions: The factors of twenty are 1, 2, 4, 5, 10, 20. Among these factors, the ones that do not exceed seven are 1, 2, 4, and 5. Therefore, there are four factors of twenty (20) that do not exceed seven.

Q.7: What two prime numbers have a difference between them that can be divided evenly into five with no remainder?
Solutions: The pair of prime numbers that satisfies this condition is (2, 7). The difference between 7 and 2 is 5, which can be divided evenly by 5 without any remainder.

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