Factors of 322

Factors of 322 are the list of integers that can be evenly divided into 322. There are 8 factors of 322 of which 322 itself is the biggest factor and its positive factors are 1, 2, 7, 14, 23, 46, 161, 322. The Prime Factors of 322 are 2 × 7 × 23 and its Factors in Pairs are (1, 322), (2, 161), (7, 46), (14, 23).

All Factors of 322: 1, 2, 7, 14, 23, 46, 161 and 322
Negative Factors of 322: -1, -2, -7, -14, -23, -46, -161 and -322
Prime Factors of 322: 2, 7, 23
Prime Factorization of 322: 2¹ × 7¹ × 23¹
Sum of Factors of 322: 576

1.	What Are the Factors of 322?
2.	Factors of 322 by Prime Factorization
3.	Factors of 322 in Pairs
4.	FAQs on Factors of 322

What are Factors of 322?

Factors of 322 are pairs of those numbers whose products result in 322. These factors are either prime numbers or composite numbers.

How to Find the Factors of 322?

To find the factors of 322, we will have to find the list of numbers that would divide 322 without leaving any remainder.

322/46 = 7; therefore, 46 is a factor of 322 and 7 is also a factor of 322.
322/2 = 161; therefore, 2 is a factor of 322 and 161 is also a factor of 322.

Similarly we can find other factors. Hence, the factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322.

☛ Also Check:

Factors of 121 - The factors of 121 are 1, 11, 121
Factors of 13 - The factors of 13 are 1, 13
Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 31 - The factors of 31 are 1, 31
Factors of 84 - The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Factors of 322 by Prime Factorization

The number 322 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 322. The first step is to divide the number 322 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

322 ÷ 2 = 161

Further dividing 161 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 161 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 322 can be written as 2¹ × 7¹ × 23¹ where 2, 7, 23 are prime.

Factors of 322 in Pairs

Pair factors of 322 are the pairs of numbers that when multiplied give the product 322. The factors of 322 in pairs are:

1 × 322 = (1, 322)
2 × 161 = (2, 161)
7 × 46 = (7, 46)
14 × 23 = (14, 23)

Negative pair factors of 322 are:

-1 × -322 = (-1, -322)
-2 × -161 = (-2, -161)
-7 × -46 = (-7, -46)
-14 × -23 = (-14, -23)

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

Factors of 322 Solved Examples

Example 1: How many factors are there for 322?

Solution:

The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322. Therefore, 322 has 8 factors.
Example 2: Find the LCM and Greatest Common Divisor (GCD) of 322 and 147.

Solution:

The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322 and factors of 147 are 1, 3, 7, 21, 49, 147.

Therefore, the LCM of 322 and 147 is 6762 and Greatest Common Divisor (GCD) of 322 and 147 is 7.
Example 3: Find if 2, 7, 111, 161 and 322 are factors of 322.

Solution:

When we divide 322 by 111 it leaves a remainder. Therefore, the number 111 is not a factor of 322. All numbers except 111 are factors of 322.
Example 4: Find the product of all the prime factors of 322.

Solution:

Since, the prime factors of 322 are 2, 7, 23. Therefore, the product of prime factors = 2 × 7 × 23 = 322.

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FAQs on Factors of 322

What are the Factors of 322?

The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322 and its negative factors are -1, -2, -7, -14, -23, -46, -161, -322.

What is the Sum of the Factors of 322?

Sum of all factors of 322 = (2^{1 + 1} - 1)/(2 - 1) × (7^{1 + 1} - 1)/(7 - 1) × (23^{1 + 1} - 1)/(23 - 1) = 576

What are the Pair Factors of 322?

The pair factors of 322 are (1, 322), (2, 161), (7, 46), (14, 23).

What is the Greatest Common Factor of 322 and 105?

The factors of 322 and 105 are 1, 2, 7, 14, 23, 46, 161, 322 and 1, 3, 5, 7, 15, 21, 35, 105 respectively.

Common factors of 322 and 105 are [1, 7].

Hence, the Greatest Common Factor of 322 and 105 is 7.

How Many Factors of 322 are also common to the Factors of 289?

Since, the factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322 and factors of 289 are 1, 17, 289. Hence, 322 and 289 have only one common factor which is 1. Therefore, 322 and 289 are co-prime.

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