The factors of 73 are the numbers when multiplied give the result as the original number. In other words, factors are the numbers that divide the original number uniformly. When two numbers on multiplication give the actual number, the numbers are called the factors. Suppose, when we multiply 5 and 6, we get 30, i.e. 5 × 6 = 30. Here, 5 and 6 are the factors of 30; also, (5, 6) is one of the factor pairs of 30. Similarly, we can find the factors of pairs of factors for any given number. In this article, you will learn how to find the factors of a number 73, factor pairs and prime factors of 73 along with examples.
What are the Factors of 73?
We know that 73 is not a composite number so it has only two factors, i.e. one and the number itself.
The factors of 73 are 1 and 73.
Factor pairs of the number 73 are the natural numbers but not a fraction or decimal number.
How to Find the Factors of 73?
To find the factors of a number, 73, we generally use the factorization method.
In the factorization method, first, consider the numbers 1 and 73 as factors for 73 and continue with finding the other pair of multiples of 73, which gives the results as an original number.
Go through the below given steps to understand the process of finding the factors of 73.
Step 1: First, write the number 73.
Step 2: Find the two numbers, which results in 73 under the multiplication, say 1 and 73, such that 1 × 73 = 73.
Step 3: As we know 1 and 73 are the prime numbers that have only two factors, i.e., one and the number itself and cannot further factorize it.
Step 4: The factors of 73 are 73 and 1.
Step 5: Therefore, the factorization of 73 is written as 73 = 73 × 1.
Factors of 73 |
1 and 73 |
Alternatively, we can find the factors of 73 by the division method. Here, we need to divide 73 by natural numbers such 1, 2, 3, and so on. When we get the remainder as 0, then the divisor in that case is the factor of 73.
73/1 = 73 (remainder = 0)
73/2 = 36.5 (factors cannot be fractions)
73/3 = 24.33
…
73/72 = 1.0134
73/73 = 1 (remainder = 0)
Thus, 1 and 73 are the only factors of 73.
Pair Factors of 73
To find the pair factors for 73, multiply the two numbers to get the original number as 73. We can write both positive and negative integers in pairs as shown in the table below:
Positive pair Factors |
Negative pair Factors |
1 × 73 = 73; (1, 73) |
(-1) × (-73) = 73; (-1, -73) |
73 × 1 = 73; (73, 1) |
(-73) × (-1) = 73; (-73, -1) |
Therefore, the positive pair factors of 73 are (1, 73) and (73, 1)
The negative pair factors of 73 are (-1, -73) and (-73, -1).
Prime Factors of 73
Generally, we use the prime factorization method to find the prime factors of a given number. We can write the prime factors of 73 as:
73 = 1 × 73
We know that 73 is a prime. We cannot factor it further since the prime numbers do not have factors other than one and the number itself.
Therefore, there are no prime factors for 73 other than 73 itself.
Some important facts about factors of 73 are listed below:
- The sum of factors of 73 is 74.
- The product of factors of 73 is equal to the number itself, i.e. 73 only.
- The number of factors of 73 is 2.
- The factors of 73 are odd numbers as 73 is an odd number.
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Examples
Example 1:
Find the common factors of 72 and 73.
Solution:
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
The factors of 73 are 1 and 73.
Thus, there is only one factor common for 72 and 73, i.e. 1.
Example 2:
What are the factors that are common to 73 and 75?
Solution:
The factors of 73 are 1 and 73.
The factors of 75 are 1, 3, 5, 15, 25 and 75.
Therefore, the only common factor of 73 and 75 is 1.
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Frequently Asked Questions on Factors of 73
How many factors does 73 have?
There are only two factors for 73 and they are 1 and 73.
Is 73 prime or composite?
The number 73 is a prime number since it has only two factors, i.e. one and the number itself.
Write the factors of 73.
The factors of 73 are 1 and 73. These can be expressed in terms of pair factors as:
1 × 73 = 73; (1, 73)
73 × 1 = 73; (73, 1)
Is 2 a factor of 73 yes or no?
No, 2 is not a factor of 73. As 73 is an odd number, all its factors will be odd. Thus, 2 is not a factor of 73 since it is an even number.
What are the pair factors of 73?
The pair factors of 73 can be written for both positive and negative integers.
The positive pair factors of 73 are (1, 73) and (73, 1).
The negative pair factors of 73 are (-1, -73) and (-73, -1).