Factors of 123 | Prime Factorization of 123 | Factor Tree of 123

Factors of 123

Factors of 123	Factor Pairs of 123	Prime factors of 123
1, 3, 41, 123	(1, 123), (3, 41)	3 x 41

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What are the factors of 123

The factors of 123 are 1, 3, 41, and 123.

To find the factors of a number, you can list out all of the numbers that divide evenly into that number. For example, to find the factors of 123, we can list out all of the numbers that divide evenly into 123: 1, 3, 41, and 123.

So, the factors of 123 are 1, 3, 41, and 123.

Note: A factor is a number that can be multiplied by another number to give a product. For example, 3 is a factor of 123 because 3 x 41 = 123.

How to Find Factors of 123

Here are four methods through which you can find the factors of 123: 

• Factors of 123 using the Multiplication Method
• Factors of 123 using the Division Method
• Prime Factorization of 123
• Factor tree of 123

Factors of 123 Using the Multiplication Method

To find the factors of 123 using the multiplication method, follow these steps:

• Start by writing the number 123 and its factors (1 and 123) in a table.
• Divide 123 by 2. If the result is not an integer, then 2 is not a factor of 123. If the result is an integer, write it in the table as a factor.
• Divide 123 by 3. If the result is not an integer, then 3 is not a factor of 123. If the result is an integer, write it in the table as a factor.
• Continue dividing 123 by each successive integer (4, 5, 6, etc.) until you reach 123. If the result of the division is an integer, write it in the table as a factor.

Here is what the table should look like:

123	1	123
123/2
61.5
—–	–	—-
123/3		41

41.0

3

41

Based on the table, we can see that the factors of 123 are 1, 3, and 41.

Note: The multiplication method is a systematic way of finding the factors of a number by dividing the number by each integer starting from 2 and checking if the result is an integer. It is a good method to use when you want to find all of the factors of a number and you don’t want to miss any. 

Factors of 123 Using the Division Method

The division method is a way of finding the factors of a number by dividing the number by each of its potential factors and checking if the result is an integer. To find the factors of 123 using the division method, follow these steps:

1. Start with the number 1, which is always a factor of any number.
2. Divide 123 by 2. Since 123 is not divisible by 2 without a remainder, move to the next number.
3. Divide 123 by 3. 123 ÷ 3 = 41. This means that 3 is a factor of 123.
4. Since 41 is a prime number, there are no further divisions to be made.
5. Therefore, the factors of 123 are 1, 3, 41, and 123.

For example:

• 123 / 1 = 123 (integer)
• 123 / 3 = 41 (integer)
• 123 / 41 = 3 (integer)
• 123 / 123 = 1 (integer)

Based on these results, we can see that the factors of 123 are 1, 3, 41, and 123.

Prime Factorization of 123

The prime factorization of 123 is the expression of a number as the product of its prime factors. To find the prime factorization of 123, we can follow these steps:

1. Divide 123 by the smallest prime number, which is 2. If the result is not an integer, move on to the next smallest prime number (3).
2. Divide the result of the division by 2 (or the next smallest prime number). If the result is not an integer, move on to the next smallest prime number.
3. Repeat this process until you are left with only prime numbers.

Here’s the process for finding the prime factorization of 123:

• 123 / 2 = 61.5 (not an integer, so 2 is not a factor of 123)
• 123 / 3 = 41 (integer, so 3 is a factor of 123)
• 41 / 2 = 20.5 (not an integer, so 2 is not a factor of 41)
• 41 / 3 = 13.6 (not an integer, so 3 is not a factor of 41)
• 41 is a prime number, so the prime factorization of 123 is 3 * 41.

So, the prime factors of 123 are 3 and 41.

Factor tree of 123

A factor tree is a visual tool used to find the prime factorization of a number. To create a factor tree for the number 123, follow these steps:

1. Write 123 at the top of the tree.
2. Divide 123 by the smallest prime number, which is 2. If the result is not an integer, move on to the next smallest prime number (3).
3. Divide the result of the division by 2 (or the next smallest prime number). If the result is not an integer, move on to the next smallest prime number.
4. Repeat this process until you are left with only prime numbers.

Here’s the process for finding the prime factorization of 123:

1. 123 / 2 = 61.5 (not an integer, so 2 is not a factor of 123)
2. 123 / 3 = 41 (integer, so 3 is a factor of 123)
3. 41 / 2 = 20.5 (not an integer, so 2 is not a factor of 41)
4. 41 / 3 = 13.6 (not an integer, so 3 is not a factor of 41)
5. 41 is a prime number, so the prime factorization of 123 is 3 * 41.

The factor tree for 123 looks like this:

Copy code

123 / \ 3 41

Factor Pairs of 123

The factor pairs of 123 are the pairs of numbers that can be multiplied together to get 123. They are (1, 123), (3, 41).

To find the factor pairs of a number, you can simply list out all of the numbers that divide evenly into that number. For example, to find the factor pairs of 123, we can list out all of the numbers that divide evenly into 123: 1, 3, 41, and 123. These numbers can then be paired up to create the factor pairs of 123.

Alternatively, you can use the division method to find the factors of a number. To do this, divide the number by each of its potential factors and check if the result is an integer. If the result is an integer, the number is a factor of 123.

For example: 

• 123 / 1 = 123 (integer)
• 123 / 3 = 41 (integer)
• 123 / 41 = 3 (integer)
• 123 / 123 = 1 (integer)

Based on these results, we can see that the factors of 123 are 1, 3, and 41. These numbers can be paired up to create the factor pairs of 123: (1, 123), (3, 41).

More Factors

• Factors of 120
• Factors of 121
• Factors of 122
• Factors of 123
• Factors of 124
• Factors of 125
• Factors of 126

Factors of 123 – Quick Recap

• Factors of 123:  1, 3, 41, 123
• Negative Factors of 123:   (1, 123), (3, 41).
• Prime Factors of 123: 3 x 41
• Prime Factorization of 123: 3 x 41

Also Check: Multiples, Square Root, and LCM

Solved Examples of Factor of 123

Q.1: If there are 119 books available at the library and 7 people want to borrow some, how many books can each person borrow?
Solution: Each person can borrow 17 books. (119/7 = 17)

Q.2: Eric has 120 marbles that he is trying to divide equally among 6 of his friends. How many will each friend receive? 
Solution: Each friend will receive 20 marbles. (120/6 = 20)

Q.3: What is the greatest common factor between 1232 and 1234? 
Solution: Prime factorization of 1232: 2^4 × 7 × 11. Prime factorization of 1234: 2 × 617. The common prime factor is 2. The product of the common prime factors is 2. Therefore, the greatest common factor (GCF) of 1232 and 1234 is 2

Q.4: Are there any prime numbers that can be multiplied together to equal 1232? 
Solution: Yes, there are prime numbers that can be multiplied together to equal 1232. The prime factorization of 1232 is 2^4 × 7 × 11. This means that 1232 can be expressed as the product of the prime numbers 2, 2, 2, 2, 7, and 11.

Q.5: If there are 123 apples for sale at the farmers market and 3 customers want some, how many apples should each customer receive? 
Solution: 123 apples ÷ 3 customers = 41 apples per customer. Therefore, each customer should receive 41 apples.

Q.6: Is 123 a prime number?  
Solution: No, 123 is not a prime number because it can be divided evenly by more than two numbers (3, 41, and 123).

Q.7: How long would it take to read a book with 120 pages if it took an average of 3 minutes per page? 
Solution:  It would take approximately 6 hours to read the entire book.

Q.8: What are the factors of 123? 
Solution: The factors of 123 are 1, 3, 41, and 123.

Q.9: How many customers can buy books if there are 123 books for sale and 5 customers want them?    
Solution: If there are 123 books for sale and 5 customers want to buy them, each customer can buy 24 books, with 3 books remaining.

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