Factors of 384

Similarly, as we learned above, factors of 384 are such numbers that will be multiplied to get 384. There are both positive and negative factors of numbers that we will learn as we move ahead in the topic.

384 has only fifteen factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, and 384.

Negative factors of 384: Negative factors are nothing but the negative counterparts of the position factors of a number.

Since 384 has sixteen positive factors:  1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192,and 384, it will also have four negative counterparts, which are -1, -2, -3, -4, -6,  -8, -12, -16, -24, -32, -48, -64, -96, -128, -192 and -384.

Prime factors of 384: Since 384 is a composite number, it has 2 and 3 as its prime factor.

Prime factorization of 384: Prime factorization of a number is the method of expressing 384 as a product of prime factors.

The prime factorization of 384 = 2⁷ × 3
 

There are several ways of finding factors of 384. We will learn about them one by one as we go on.
 

In this method, we will try to find such a pair of numbers that will give 384 as their product. We recommend that you should follow the following steps to find factors using multiplication.

Step 1: Always look for a pair of numbers whose product is 384.

Step 2: After finding such pairs, list them all one by one.

Here, factor pairs of 384 are (1, 384), (2, 192), (3, 128), (4, 96), (6, 64), (8, 48), (12,32) and (16,24). 

So the factors of 384 are 1, 2, 3, 4, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192,and 384
 

In the method, we need to find such numbers that divide 384 completely without leaving any remainder.

384/1 = 384

384/ 2 = 89

384/ 3 = 128

384/ 4 = 96

384/ 8 = 48

384/ 12 = 32

384/ 16 = 24

384/ 24 = 16

384/ 32 = 12

384/ 48 = 8

384/ 64 = 6

384/ 96= 4

384/ 128 = 3

384/ 192 = 2

384/ 384 = 1

All the 16 numbers:  1, 2, 3, 4, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, and 384 mentioned above divide 384 completely without any remainder. Hence, they are factors of 384.
 

In the prime factorization method, a number is expressed as the product of prime factors.

Here, as we know, 384 = 2⁷ × 3

 2⁷ and 3 are the prime factors when multiplied together will give 384 as a product of the multiplication.
 

A factor tree is a graphical representation of factors of any number. In the diagram, each branch represents the prime factors a number has.
 

The factor pairs of a number refer to a pair of numbers which, when multiplied, will give the number as a product.

 The factor pairs of 384 are (1, 384)  (1, 384), (2, 192), (3, 128), (4, 96), (6, 64), (8, 48), (12,32) and (16,24).

 
Positive Pair Factors of 384 are (1, 384),  (2, 192), (3, 128), (4, 96), (6, 64), (8, 48), (12,32) and (16,24).

 
Negative Pair Factors of 384 are (-1, -384), (-2, -192), (-3, -128), (-4, -96), (-6,- 64), (-8, -48), (-12, -32) and (-16, -24).
 
 

• Prime Numbers: Those numbers which have no other factors other than 1 & the number itself.

• Composite Numbers: Those numbers that have more than 2 factors.

• Negative Factors: These are the counterparts of the positive factors of a number.

• Prime Factorization: Process of breaking down a composite number into products of several of its prime factors.