Factors of 81 | Prime Factorization of 81 | Factor Tree of 81

Factors of 81 

Factors of 81	Factor Pairs of 81	Prime factors of 81
1, 3, 9, 27, 81	(1,81) (3,27) (9,9) (27,3)	3 x 3 x 3 x 3

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What are the factors of 81?

The factors of 81 are 1, 3, 9, 27, and 81.

To find the factors of a number, you can divide the number by each whole number from 1 to the number itself. For example, to find the factors of 81, you can divide 81 by each whole number from 1 to 81. If the result of the division is a whole number, then the number you divided by is a factor of 81. In this case, the whole numbers that divide evenly into 81 are 1, 3, 9, 27, and 81.

How to Find Factors of 81

Here are four methods that you can use to find the factors of 81:

1. Factors of 81 using the Multiplication Method
2. Factors of 81 using the Division Method
3. Prime Factorization of 81
4. Factor tree of 81

Factors of 81 Using the Multiplication Method

The factors of a number are the numbers that can be multiplied together to produce that number. For example, the factors of 8 are 1, 2, 4, and 8, because 1 x 8 = 8, 2 x 4 = 8, and 4 x 2 = 8.

To find the factors of a number using the multiplication method, you can start by writing down the number itself. Then, you can try to find two other whole numbers whose product is equal to the original number.

For example, to find the factors of 81, you can start by writing down 81. Then, you can try to find two other whole numbers whose product is 81. One way to do this is to start with the number 1 and multiply it by 81 to get 81. Another way is to start with the number 3 and multiply it by 27 to get 81. You can continue finding pairs of numbers whose product is 81 by multiplying smaller and smaller numbers together. For example, you can multiply 9 by 9 to get 81, or you can multiply 6 by 13 to get 78.

Using the multiplication method, you can find all the pairs of numbers whose product is the original number. For example, the factors of 81 using the multiplication method are 1 and 81, 3 and 27, 9 and 9, and so on. You can continue finding pairs of numbers whose product is 81 until you reach the number itself.

Factors of 81 Using the Division Method

To find the factors of a number using the division method, you can start by dividing the number by the smallest possible whole number (which is usually 1). If the result is a whole number, then that number is a factor of the original number. If the result is not a whole number, you can divide the original number by the next whole number and see if that result is a whole number. You can continue doing this until you reach the original number itself.

For example, to find the factors of 81 using the division method, you can start by dividing 81 by 1. The result, 81, is a whole number, so 1 is a factor of 81. Next, you can divide 81 by 2. The result, 40.5, is not a whole number, so 2 is not a factor of 81. You can continue dividing 81 by 3, 4, 5, and so on until you reach 81. The whole numbers that divide evenly into 81 are 1, 3, 9, 27, and 81. These are the factors of 81 using the division method.

Another way to use the division method is to start with the number itself and divide it by the largest possible whole number. For example, to find the factors of 81, you can start by dividing 81 by 81. The result, 1, is a whole number, so 81 is a factor of 81. You can then divide 81 by 80, 79, 78, and so on until you reach 1. The whole numbers that divide evenly into 81 are 1, 3, 9, 27, and 81. These are the factors of 81 using the division method.

Prime Factorization of 81

The prime factorization of a number is the expression of that number as the product of its prime factors. A prime factor is a whole number that is greater than 1 and is only divisible by 1 and itself. For example, the prime factors of 8 are 2 and 2, because 8 can be expressed as the product of two 2s (2 * 2 = 8).

To find the prime factorization of a number, you can start by dividing the number by the smallest possible prime number. If the result is not divisible by that prime number, you can move on to the next smallest prime number and continue until you reach a prime number that cannot be divided any further.

For example, to find the prime factorization of 81, you can start by dividing 81 by the smallest prime number, which is 2. However, 81 is not divisible by 2, so we move on to the next smallest prime number, which is 3. 81 is divisible by 3, so we divide 81 by 3 to get 27. 27 is also divisible by 3, so we divide it by 3 again to get 9. 9 is divisible by 3, so we divide it by 3 one more time to get 3. 3 is a prime number, so we can’t divide it any further.

The prime factorization of 81 is 3^4, which means that 81 can be expressed as the product of four 3s. Another way to write the prime factorization of 81 is 3 * 3 * 3 * 3.

Factor tree of 81

To create a factor tree, you can start with the number you want to find the factors of (in this case, 81) and then find two other whole numbers whose product is equal to that number. For example, 81 can be expressed as the product of 3 and 27, so you can write those numbers on the next level of the tree. Then, you can find two other whole numbers whose product is equal to 27, and so on, until you reach a number that is a prime number (a prime number is a whole number greater than 1 that is only divisible by 1 and itself).

Using a factor tree, you can easily find all the factors of a number, as well as its prime factorization. In this case, the factors of 81 are 1, 3, 9, 27, and 81, and its prime factorization is 3^4.

Factor Pairs of 81

A factor pair of a number is a pair of whole numbers whose product is equal to that number. For example, the factor pairs of 8 are (1, 8) and (2, 4), because 1 x 8 = 8 and 2 x 4 = 8.

To find the factor pairs of a number, you can start by finding the factors of that number using the multiplication or division method. Then, you can pair up the factors in different ways to create all the possible factor pairs.

For example, to find the factor pairs of 81, you can start by finding the factors of 81, which are 1, 3, 9, 27, and 81. Then, you can pair up the factors in different ways to create the factor pairs: (1, 81), (3, 27), and (9, 9). These are all the possible factor pairs of 81.

Another way to find the factor pairs of a number is to use a visual representation, such as a factor tree or a multiplication table. A factor tree shows the factors of a number in a tree-like structure, while a multiplication table shows the factors of a number in a grid. By looking at the factors in these different formats, you can easily see all the possible factor pairs.

More Factors

• Factors of 78
• Factors of 79
• Factors of 80
• Factors of 81
• Factors of 82
• Factors of 83
• Factors of 84

Factors of 81 – Quick Recap

• Factors of 81: 1, 3, 9, 27, and 81.
• Negative Factors of 81: -1, -3, -9, -27, and -81.
• Prime Factors of 81:   3
• Prime Factorization of 81: 3 × 3 × 3 × 3

Factors of 81 – Fun Facts

• 81 is a perfect square, which means that it is the product of two equal whole numbers. In this case, 81 is the square of 9, because 9 x 9 = 81.
• The factors of 81 include 1 and 81, which are known as the co-factors of 81. Co-factors are pairs of numbers that, when multiplied together, produce the original number. In this case, 1 and 81 are the co-factors of 81, because 1 x 81 = 81.
• The factors of 81 can be arranged in a multiplication table, which is a grid that shows the product of two numbers for different combinations of those numbers.

Also Check: Multiples, Square Root, and LCM

Solved Examples of Factor of 81

Q.1: What is the greatest common factor between 81 and 27?
Solution: The greatest common factor (GCF) between 81 and 27 is 9, as both 81 and 27 are divisible by 9 without a remainder.

Q.2: How many negative factors does the number 81 have?
Solution: There are 5 negative factors of 81; -1, -3, -9, -27, -81.

Q.3: Is there a difference between the factors and multiples of 81? 
Solution: While factors and multiples have similar definitions in that they both refer to groups or collections of related numbers generated by multiplying or dividing a given number, there is an important difference between them – factors refer to how many times the original number can be divided evenly while multiples make reference to how many times it has been multiplied by itself.

Q.4: Find two equal numbers that multiply together to equal 81.
Solution: Two numbers that multiply together to equal 81 are 9 and 9; 9 x 9 = 81.

Q.5: Which number from 1-81 divides into it without any remainders?
Solution: Any number from 1-81 can divide into it with no remainders, but some will produce fractions or decimals instead of a whole number result.  

Q.6: What is the least common multiple (LCM) of 81 and 27?
Solution: Prime factorization of 81: 81 = 3^4. Prime factorization of 27: 27 = 3^3. To find the LCM, we take the highest power of each prime factor:, The highest power of 3: 3^4. LCM(81, 27) = 3^4 = 81. Therefore, the LCM of 81 and 27 is 81.  

Q.7: What is the sum of all positive integer divisors for 81?   
Solution: The sum of the positive integer divisors for 81 is 121; 1+3+9+27+81 = 121.

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Frequently Asked Questions on Factors of 81