Didyou know that 336is an even composite number whose prime factorization consists ofthree prime numbers,2, 3, and 7? The sum of theprime factors of 336 is 12, which is again a composite number. In this chapter, we will calculate the factors of 336, the prime factors of 336, and the factors of 336in pairs along with solved examples and interactive questions.

**Factors of 336:**1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336.**Prime Factorization of 336:**336= 2^{4}× 3× 7

1. | What Are the Factors of 336? |

2. | How to Calculate the Factors of 336? |

3. | Factors of 336 by Prime Factorization |

4. | Factors of 336 in Pairs |

5. | FAQs on Factors of 336 |

## What Are the Factors of 336?

The factors of 336are the numbers which onmultiplication give336.These are thenumbers which divide 336without leaving any remainder. Hence, when we multiplyany two whole numbers with each other and obtain 336 as the answer, boththenumbers are said to be the factors of 336.

## How to Calculate the Factors of 336?

We can calculate the factors of 336 byfinding all the numbers which divide 336without leaving any remainder. Let's start by checking the factors of 336, starting from 1. We can express 336as a product of its prime factors in the prime factorization method and we can divide 336with its divisors in the division method. For the numbers dividing336 entirely, the divisors as well as their quotients are the factors of 336.

Numbers dividing 336 | Factors of 336 |
---|---|

336/1 = 336 | 1 and 336 are factors of 336 |

336/2 = 168 | 2 and 168 are factors of 336 |

336/3 = 112 | 3 and 112 are factors of 336 |

336/4 = 84 | 4 and 84 are factors of 336 |

336/6 = 56 | 6 and 56 are factors of 336 |

336/7 = 48 | 7 and 48 are factors of 336 |

336/8 = 42 | 8 and 42 are factors of 336 |

336/12 = 28 | 12 and 28 are factors of 336 |

336/14 = 24 | 14 and 24 are factors of 336 |

336/16 = 21 | 16 and 21 are factors of 336 |

Hence,the **factors of 336are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168 and 336.**

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

- Factors of 168- The factors of 168are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
- Factors of 112- The factors of 112are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
- Factors of 84- The factors of 84are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
- Factors of 36- The factors of 36are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- Factors of 42- The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
- Factors of 21- The factors of 21are 1, 3, 7, and 21.

## Factors of 336 by Prime Factorization

Whena composite number is expressed as the product of itsprime factors, it is called as prime factorization. To get the prime factorization of 336, we use two methods:

- Method 1: Factor Tree Method
- Method 2: Upside Down Division Method

### Method 1: Factor Tree Method

Factor tree of 336is:

### Method 2: Upside Division Method

We divide 336by its smallest prime factor which is 2

336/2= 168

168is divided by its smallest prime factor and the quotient is obtained. This process is repeated till we get the quotient as 1. Thus, the prime factorization of 336is:

Hence, the prime factors of 336are2, 3, and 7.

The prime factorization of 336is2^{4}× 3× 7.

## Factors of 336 in Pairs

The pair of numbers which on multiplicationgive336are the factor pairs of 336. Let's observe the following factorsof 336in pairs. Thenegative pair factors of 336 are obtained when theproduct of two negative numbers is taken( - ve × - ve ) = +ve.

- Positive Pair Factors of 336are: (1, 336), (2, 168), (3, 112), (4, 84), (6, 56), (7, 48),(8, 42), (12, 28), (14, 24),(16, 21)
- Negative Pair Factors of 336are: (-1, -336), (-2, -168), (-3, -112), (-4, -84), (-6, -56), (-7, -48),(-8, -42), (-12, -28), (-14, -24),(-16, -21)

**Important Notes:**

- As 336ends withits last two digits as 36and 36is divisible by 4, we can say that4 is one of the factors of 336.
- As the sum of the digits of 336 is 12, one of the factors of 336 is 3.
- 336 is a non-perfect square number. Hence, it has even number of factors.

**Challenging Questions:**

- Are 672 and 3/4factors of 336? Why do you think so?

## FAQs on Factors of 336

### What are thefactorsof 336?

The factors of 336are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336.

### What are the prime factors of 336?

The prime factors of 336are 2, 3, and 7.

### Are all the factors of 336prime?

No, all the factors of 336are not prime.

### What are the common factors of 336and 440?

The factors of 336are1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336.

The factors of 440are1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220 and 440.

Hence, the common factors of 336and 440are 1, 2,4 and 8.

### Is 9a factor of 336?

No, 9is not a factor of 336.