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Factors of 92

Prime factors of 92 are 2 and 23. Factors are the numbers that, when multiplied in pairs, give the product as 92. Few of these factors are positive and a few are negative as well. It also is an even composite number, which means that it has several factors. In this lesson, we will calculate the factors of 92 and learn about the prime factors of 92 and factors of 92 in pairs along with solved examples for a better understanding.

Factors of 92: 1, 2, 4, 23, 46, and 92
Prime Factorization of 92: 92 =  22 x 23

1. What Are the Factors of 92?
2. How to Calculate the Factors of 92?
3. Factors of 92 by Prime Factorization
4. Factors of 92 in Pairs
5. FAQs on Factors of 92

What Are the Factors of 92?

Factors of a number n are the numbers that completely divide the number n. t means that if the remainder is zero, then the number is the factor of 92. We are talking about factors of the number 92 here. Let's first see the numbers that completely divide 92.

The numbers that divide 92 completely are 1, 2, 4, 23, 46, and 92.

Factors of 92

Explore factors using illustrations and interactive examples.

How to Calculate the Factors of 92?

Factors of the number 92 can be calculated as follows:

  • Write the smallest factor of 92 (except for 1). The smallest factor of 92 is 2, Therefore, 92 ÷ 2 = 46. So, 2 and 46 are the factors of 92.

  • Write the next smallest factor of 92. The next smallest factor of 92 is 4. Therefore, 92 ÷ 4 = 23. So, 4 and 23 are the factors of 92.

  • Include 1 and the number itself to write all the factors.

Factors of 92 are 1, 2, 4, 23, 46, and 92.

Important Notes

  • The prime factors of a number are different from their factors.
  • If a number n has an odd number of positive factors, then n is a perfect square.
  • 1 and the number itself are also the factors of any number.
  • There are no factors of a number n  between n and n/2.
  • The number that has more than 2 factors is called composite number.
  • 1 is not a prime number; 2 is the smallest prime number.

Factors of 92 by Prime Factorization

The prime factorization method to calculate the factors of any number is one of the most important methods. Many students prefer using prime factorization while performing calculations.

In the prime factorization method, we can only factorize a number into its prime factors.


Factor tree of 92

Prime factorization of 92 are 92 = 2 × 2 × 23. Let's write all the factors of 92 using prime factors.

  • Take all the numbers (2, 2, and 23) and multiply only two at a time, 2 × 2 = 4 and 2 × 23= 46. Factors obtained are 4 and 46.

  • Write all the factors of the number: 1, 2, 4, 23, 46, 96

Factors of 92 in pairs

The pair of factors of number 92 is the set of two numbers which, when multiplied together, give the number 92.

Factors of 92 are 1, 2, 4, 23, 46, 92

Factors of 92 in pairs are (1, 92), (2, 46), (4, 23)

Factors of 92 in pairs

Negative factors of  92 are -1, -2, -4, -23, -46, -92

Similarly pairs of negative factors of 92 are: (-1, -92), (-2, -46), (-4, -23)

 

Solved Examples

 

  1. Example 1 Help Tom to find the sum of all the positive factors of 92.

    Solution

    Positive factors of 92 are: 1, 2, 4, 23, 46, 92

    Sum of all the factors is 1 + 2 + 4 + 23 + 46 + 92 = 168.

    Therefore, sum of all the positive factors of 92 is 168.

  2. Example 2 Paul says that there exist only two common factors between 72 and 92, while Chris says there exist three common factors between these numbers. Who is correct?

    Solution

    Let's first write the factors of 72 and 92

    Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
    Factors of 92 are 1, 2, 4, 23, 46, 92

    Common factors are 1, 2, 4
    There are three common factors between 72 and 92.

    Hence, Chris is correct. 72 and 92 have three common factors..

  3.  

    Example 3 If factors of 92 are arranged in ascending order, the product of two middle factors obtained is P. If the factors are arranged in descending order, the product of two middle factors obtained is Q. Check whether P = Q or not.

    Solution

    Factors of 92 are 1, 2, 4, 23, 46, 92

    Factors of 92 arranged in ascending order: 1, 2, 4, 23, 46, 92
    Middle two factors are 4 and 23
    4 × 23 = 92
    P = 92

    Factors of 92 arranged in descending order: 92, 46, 23, 4, 2, 1
    Middle two factors are: 23 and 4
    23 × 4 = 92
    Q = 92

    Hence, P = Q.

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FAQs on Factors of 92

1. What is the highest common factor of 92 and 42?

Factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 92 are: 1, 2, 4, 23, 46, 92
Common factors between 42 and 92 are: 1, 2
HCF (42 and 92) is 2.

2. What are the common factors of 92 and 72?

Factors of 92 are: 1, 2, 4, 23, 46, 92
Factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Common factors between 92 and 72 are: 1, 2, 4

3. What are the factors of 92?

The factors of 92 are 1, 2, 4, 23, 46, 92.

4. What are the common factors of 36 and 92?

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 92 are 1, 2, 4, 23, 46, 92
Common factors of 36 and 92 are 1, 2, 4
HCF of 36 and 92 is 4.

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