Do you know, the number 128 has three perfect squares as its factors? These include 4, 16, and 64. In all, it has 8 factors. In this lesson, we will calculate the factors of 128, prime factors of 128, and factors of 128 in pairs along with solved examples for a better understanding.

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**Factors of 128:**1, 2, 4, 8, 16, 32, 64, and 128

**Prime Factorization of 128:**128 = 27

1. | What Are the Factors of 128? |

2. | How to Calculate the Factors of 128? |

3. | Factors of 128 by Prime Factorization |

4. | Factors of 128 in Pairs |

5. | Important Notes |

6. | FAQs on Factors of 128 |

## What Are the Factors of 128?

The factor of a number is that number which divides the given number completely, i.e., it leaves no remainder. To find the factors of the number 128, we will have to perform division on 128 and find the numbers which divide 128 completely, leaving no remainders.

All the divisors which give remainder 0 for our number 128 are the factors of 128. The diagram below provides the representation of the above definition.

## How to Calculate the Factors of 128?

To calculate the factors of any number, here in this case 128, we need to find all the numbers that would divide 128 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, 6, 7, etc. up to 64 (half of 128).

The number 1 and the number itself would always be the factors of the given number. Refer to the following table to check division of 128 by its factors:

DivisionFactor128/1 | Remainder = 0 Hence, factor = 1 |

128/2 | Remainder = 0 Hence, factor = 2 |

128/3 | Remainder = 2 3 is not a factor. |

128/4 | Remainder = 0 Hence, factor = 4 |

128/8 | Remainder = 0 Hence, factor = 8 |

128/16 | Remainder = 0 Hence, factor = 16 |

128/32 | Remainder = 0 Hence, factor = 32 |

128/64 | Remainder = 0 Hence, factor = 64 |

128/128 | Remainder = 0 Hence, factor = 128 |

Hence, the **factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.**

**Explore factors using illustrations and interactive examples.**

## Factors of 128 by Prime Factorization

Prime factorization of a number refers to breaking down a number into the form of products of its prime factors. There are different methods that can be used to find the prime factorization of a number and hence its prime factors.

To find prime factors of 128 using the division method,

**Step2.**After finding the smallest prime factor of the number 128, i.e. 2, divide 128 by 2 to obtain the quotient (64).

128/2 = 64

**Step3.**Repeat step1 with the obtained quotient (64) and continue until you get 1 as the quotient. Again, the prime factor for 64 would be 2.

64/2 = 32

Similarly,

32/2 = 16

16/2 = 8

8/2 = 4

4/2 = 2

2/2 = 1

So, the prime factorization of 128 is:

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

or

128 = 27

We can follow the same procedure using the factor tree as shown in the diagram given below:

So, the prime factorization of 128 is:

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

or

128 = 27

Further, find the products of the multiplicands in different orders to obtain the composite factors of the number. Thus, the total factors can be written including both the prime and composite numbers together as 1, 2, 4, 8, 16, 32, 64, and 128.

## Factors of 128 in Pairs

Pair factors are the factors of a number given in pairs which, when multiplied together, give that original number. The pair factors of 128 would be the two numbers which get multiplied together to result in the value of 128.The following table represents the calculation of pair factors of 128.

Factor PairPair Factorization1 and 128 | 1 × 128 = 128 |

2 and 64 | 2 × 64 = 128 |

4 and 32 | 4 × 32 = 128 |

8 and 16 | 8 × 16 = 128 |

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 128.The negative factor pairs of 128 would be ( -1, -128 ), ( -2, -64), ( -8, -16), and ( -4, -32).

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**Important Notes:**