Factors of 231 are the list of integers that we can split evenly into 231. There are total 8 factors of 231 i.e. 1, 3, 7, 11, 21, 33, 77, 231. The Prime Factors of 231 are 3 × 7 × 11 and its Factors in Pairs are (1, 231), (3, 77), (7, 33), (11, 21).

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**All Factors of 231:** 1, 3, 7, 11, 21, 33, 77 and 231 **Negative Factors of 231:** -1, -3, -7, -11, -21, -33, -77 and -231 **Prime Factors of 231:** 3, 7, 11 **Prime Factorization of 231:** 31 × 71 × 111 **Sum of Factors of 231:** 384

1. | What Are the Factors of 231? |

2. | Factors of 231 by Prime Factorization |

3. | Factors of 231 in Pairs |

4. | FAQs on Factors of 231 |

## What are Factors of 231?

Factors of 231 are pairs of those numbers whose products result in 231. These factors are either prime numbers or composite numbers.

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### How to Find the Factors of 231?

To find the factors of 231, we will have to find the list of numbers that would divide 231 without leaving any remainder.

231/231 = 1; therefore, 231 is a factor of 231.231/77 = 3; therefore, 77 is a factor of 231. Similarly we can find other factors. Hence, the factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231.

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## Factors of 231 by Prime Factorization

The number 231 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 231. The first step is to divide the number 231 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder. 231 ÷ 3 = 77

Further dividing 77 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 77 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 231 can be written as 31 × 71 × 111 where 3, 7, 11 are prime.

## Factors of 231 in Pairs

Pair factors of 231 are the pairs of numbers that when multiplied give the product 231. The factors of 231 in pairs are:

1 × 231 = (1, 231) 3 × 77 = (3, 77) 7 × 33 = (7, 33) 11 × 21 = (11, 21)

Negative pair factors of 231 are:

-1 × -231 = (-1, -231) -3 × -77 = (-3, -77) -7 × -33 = (-7, -33) -11 × -21 = (-11, -21)

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

## Factors of 231 Solved Examples

**Example 1: How many factors are there for 231?**

**Solution:**

The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. Therefore, 231 has 8 factors.

** Example 3: Find if 1, 3, 7, 51 and 77 are factors of 231.**

**Solution:**

When we divide 231 by 51 it leaves a remainder. Therefore, the number 51 is not a factor of 231. All numbers except 51 are factors of 231.

** Example 4: Find the product of all the prime factors of 231.**

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**Solution:**

Since, the prime factors of 231 are 3, 7, 11. Therefore, the product of prime factors = 3 × 7 × 11 = 231.

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## FAQs on Factors of 231

### What are the Factors of 231?

The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231 and its negative factors are -1, -3, -7, -11, -21, -33, -77, -231.

### What is the Sum of Factors of 231?

Sum of all factors of 231 = (31 + 1 – 1)/(3 – 1) × (71 + 1 – 1)/(7 – 1) × (111 + 1 – 1)/(11 – 1) = 384

### What numbers are the Pair Factors of 231?

The pair factors of 231 are (1, 231), (3, 77), (7, 33), (11, 21).

### What is the Greatest Common Factor of 231 and 31?

The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231 and the factors of 31 are 1, 31. 231 and 31 have only one common factor which is 1. This implies that 231 and 31 are co-prime. Hence, the Greatest Common Factor (GCF) of 231 and 31 is 1.

### What are the Common Factors of 231 and 44?

Since, the factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231 and the factors of 44 are 1, 2, 4, 11, 22, 44. Hence, <1, 11> are the common factors of 231 and 44.

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