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Factors of 123

Factors of 123 are the list of integers that we can split evenly into 123. There are 4 factors of 123, which are 1, 3, 41, 123. Here, 123 is the biggest factor. The Prime Factors of 123 are 3 × 41 and its Factors in Pairs are (1, 123), (3, 41).

All Factors of 123: 1, 3, 41 and 123
Negative Factors of 123: -1, -3, -41 and -123
Prime Factors of 123: 3, 41
Prime Factorization of 123: 3¹ × 41¹
Sum of Factors of 123: 168

1.	What Are the Factors of 123?
2.	Factors of 123 by Prime Factorization
3.	Factors of 123 in Pairs
4.	FAQs on Factors of 123

What are Factors of 123?

Factors of 123 are pairs of those numbers whose products result in 123. These factors are either prime numbers or composite numbers.

How to Find the Factors of 123?

To find the factors of 123, we will have to find the list of numbers that would divide 123 without leaving any remainder.

123/3 = 41; therefore, 3 is a factor of 123 and 41 is also a factor of 123.
123/123 = 1; therefore, 123 is a factor of 123 and 1 is also a factor of 123.

Similarly we can find other factors. Hence, the factors of 123 are 1, 3, 41, 123.

☛ Also Check:

Factors of 80 - The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Factors of 108 - The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 5 - The factors of 5 are 1, 5
Factors of 99 - The factors of 99 are 1, 3, 9, 11, 33, 99
Factors of 51 - The factors of 51 are 1, 3, 17, 51

Factors of 123 by Prime Factorization

The number 123 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 123. The first step is to divide the number 123 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.

123 ÷ 3 = 41

Further dividing 41 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 41 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 123 can be written as 3¹ × 41¹ where 3, 41 are prime.

Factors of 123 in Pairs

Pair factors of 123 are the pairs of numbers that when multiplied give the product 123. The factors of 123 in pairs are:

1 × 123 = (1, 123)
3 × 41 = (3, 41)

Negative pair factors of 123 are:

-1 × -123 = (-1, -123)
-3 × -41 = (-3, -41)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 123 Solved Examples

Example 1: How many factors are there for 123?

Solution:

The factors of 123 are 1, 3, 41, 123. Therefore, 123 has 4 factors.
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 123 and 78.

Solution:

The factors of 123 are 1, 3, 41, 123 and factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78.

Therefore, the Least Common Multiple of 123 and 78 is 3198 and Greatest Common Divisor (GCD) of 123 and 78 is 3.
Example 3: Find if 3, 41 and 77 are factors of 123.

Solution:

When we divide 123 by 77 it leaves a remainder. Therefore, the number 77 is not a factor of 123. All numbers except 77 are factors of 123.
Example 4: Find the product of all the prime factors of 123.

Solution:

Since, the prime factors of 123 are 3, 41. Therefore, the product of prime factors = 3 × 41 = 123.

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FAQs on Factors of 123

What are the Factors of 123?

The factors of 123 are 1, 3, 41, 123 and its negative factors are -1, -3, -41, -123.

What is the Sum of the Factors of 123?

All the Factors of 123 are 1, 3, 41, 123 and therefore the sum of all these factors is 1 + 3 + 41 + 123 = 168

What Numbers are the Prime Factors of 123?

The prime factors of 123 are 3, 41.

What is the Greatest Common Factor of 123 and 28?

The factors of 123 are 1, 3, 41, 123 and the factors of 28 are 1, 2, 4, 7, 14, 28. 123 and 28 have only one common factor which is 1. This implies that 123 and 28 are co-prime.

Hence, the Greatest Common Factor (GCF) of 123 and 28 is 1.

How Many Factors of 75 are also common to the Factors of 123?

Since, the factors of 123 are 1, 3, 41, 123 and the factors of 75 are 1, 3, 5, 15, 25, 75.
Hence, [1, 3] are the common factors of 123 and 75.

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