Factors of 92 Using Prime Factorization
What are the Factors of 92?
If the number 92 is divided by a natural number such that the remainder is zero, then the natural number is known as a factor of 92. Here, the quotient obtained on division is also a factor of 92.
The factors of 92 are 1, 2, 4, 23, 46, and 92, because all these numbers divide the number 92 evenly.
Factors | Pair Factors | Prime Factorization |
|---|---|---|
1, 2, 4, 23, 46 and 92 | (1, 92), (2, 46), (4, 23) | 2, 23 |
List of Factors of 92
To find out the total number of factors of 92 we need to follow both divisibility rules and division facts of natural numbers.
Divisor | Is the number a factor of 92 | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of all number | 1 \(\times\) 92 = 92 |
2 | Yes, 92 is even | 2 \(\times\) 46 = 92 |
3 | No, 9 + 2 = 11 is not divisible by 3 | — |
4 | Yes, 92 \(\div\) 4 = 23 Remainder = 0 | 4 \(\times\) 23 = 92 |
5 | No, the ones digit is neither 5 nor 0. | — |
6 | No, 92 \(\div\) 6 = 15 and Remainder = 2 | — |
7 | No, 92 \(\div\) 7 = 13 and Remainder = 1 | — |
8 | No, 92 \(\div\) 8 = 11 and Remainder = 4 | — |
9 | No, 92 \(\div\) 9 = 10 and Remainder = 2 | — |
10 | No, 92 \(\div\) 10 = 9 and Remainder = 2 | — |
From the above table we can conclude that the Factors of 92 are 1, 2, 4, 23, 46 and 92.
Prime Factorisation of 92
If a natural number can be expressed as a product of prime numbers, these prime numbers are known as the prime factors of that natural number. The process of expressing a number as the product of its prime factors is known as prime factorization.
The prime factorization of 92 can represented by a factor tree as shown below:
From the above prime factorisation of 92 we find that the prime factors of 92 are 2, 2 and 23.
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Factor Pairs
A factor pair of a number is a set of two factors of a number such that their product is the number itself.
Positive factor of 92 | Positive factor pair of 92 |
|---|---|
1 \(\times\) 92 = 92 | (1, 92) |
2 \(\times\) 46 = 92 | (2, 46) |
4 \(\times\) 23 = 92 | (4, 23) |
Rapid Recall
The factors of 92 are 1, 2, 4, 23, 46 and 92.
Solved Factors of 92 Examples
Example 1: Find the common factors of 92 and 100.
Solution:
The factors of 92 are 1, 2, 4, 23, 46 and 92.
The factors of 100 are 1, 2, 4, 5, 10, 20, 50 and 100.
So, the common factors of 92 and 100 are 1, 2 and 4.
Example 2 : Find the greatest common factor of 92 and 138.
Solution:
The factors of 92 are 1, 2, 4, 23, 46 and 92.
The factors of 138 are 1, 2, 3, 6, 23, 46, 69 and 138.
The common factors of 92 and 138 are 1, 2, 23 and 46, the greatest among them is 46.
So, the greatest common factor of 92 and 132 is 46.
Example 3: Can you help Alice to find the width of a rectangle if the area and length of the rectangle are 92 square inches and 23 inches, respectively.
Solution:
\(A~=~l~\times~b\) Write the formula for area of rectangle
\(92~=~23~\times~b\) Substitute 92 for A and 23 for l
\(\frac{92}{23}~=~\frac{23~\times~b}{23}\) Divide each side by 23
\(6~=~b\) Simplify
So, the width of the rectangle is 6 inches.
The negative factor pairs are of 92 are, (-1, -92), (-2, -46) and (-4, -23)
The factors of a number are divisors that exactly divide the number, that is, leaves zero as the remainder.
The prime factor of a number is a factor of the number that is also the prime number.
Example: The factors of 48 are 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 and 48.
And the prime factors of 48 are 2 , 3
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72
Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216
Therefore, the common factors of 72 and 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Two prime numbers are said to be twin prime or prime pairs if they have a difference of 2 between them.
Example: (3 and 5), (5 and 7), (11, 13), (17, 19).