# Factors And Prime Factors of 24, 28, 40, 42, 45, 56

24, 28, 40, 42, 45, and 60 are examples I will solve under factors and prime factorization. It is important to note that your knowledge of multiplication and division will aid your understanding.

To find the factor of a number, you will look for numbers that can divide the number completely.

To Find Prime Factors Of A Number

- Find the smallest prime number that can divide the number completely without leaving a reminder.
- Similarly, divide the quotient of step 1 by the smallest prime number.
- Repeat step 2 until the quotient becomes 1.
- Finally, multiply all the prime factors that are the divisors.

**24**

The factors of 24 are the numbers that are multiplied in pairs, resulting in the number 24. In other words, the numbers that divide 24 exactly are the factors of 24.

24/1 = 24

24 /2 = 12

24/3 = 8

24/4 = 6

24/6 = 4

24/8 = 3

24/12 = 2

24/24 = 1

So factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

The smallest prime number that can divide 24 completely is 2. 24/2 = 12. After that you will find another smallest prime number that can divide 12 completely. It is still 2, 12/2 = 6. Another smallest prime number that can divide 6 is 2, 6/2 = 3. Finally divide by 3 because 3 is the smallest number that can divide 3 without giving a reminder.

divisors | quotient |

2 | 24 |

2 | 12 |

2 | 6 |

3 | 3 |

1 |

The divisors are 2, 2, 2, 3, which will then multiply each other = 2 x 2 x 2 x 3

So, the prime factorization of 24 = 2 x 2 x 2 x 3 = 2^{3} x 3

**28**

The factors of 28 are the numbers that are multiplied in pairs, resulting in the number 28. In other words, the numbers that divide 28 exactly are the factors of 28.

28/1 = 28

28 /2 = 14

28/4 = 7

28/7= 4

28/14 = 2

28/28 = 1

So factors of 28 are 1, 2, 4, 7, 14, 28

The prime factor of 28

divisors | quotient |

2 | 28 |

2 | 14 |

7 | 7 |

1 | |

The divisors are 2, 2, 7, which will then multiply each other = 2 x 2 x 7

So, the prime factorization of 28 = 2 x 2 x 7 = 2^{2} x 7

**40**

The factors of 40 are the numbers that are multiplied in pairs, resulting in the number 40. In other words, the numbers that divide 40 exactly are the factors of 40.

40/1 = 40

40 /2 = 20

40/4 = 10

40/5 = 8

40/8 = 5

40/10 = 4

40/20 = 2

40/40 = 1

So factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

The prime factors of 40

divisors | quotient |

2 | 40 |

2 | 20 |

2 | 10 |

5 | 5 |

1 |

The divisors are 2, 2, 2, 5, which will then multiply each other = 2 x 2 x 2 x 5

So, the prime factorization of 40 = 2 x 2 x 2 x 5 = 2^{3} x 5

**42**

The factors of 42 are the numbers multiplied in pairs, resulting in the number 42. In other words, the numbers that divide 42 exactly are the factors of 42.

42/1 = 42

42 /2 = 21

42/3 = 14

42/6= 7

42/7 = 6

42/14 = 3

42/21 = 2

42/42 = 1

So factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The prime factors of 42

divisors | quotient |

2 | 42 |

3 | 21 |

7 | 7 |

1 | |

The divisors are 2, 3, 7, which will then multiply each other = 2 x 3 x 7

So, the prime factorization of 28 = 2 x 3 x 7

**45**

The factors of 45 are the numbers that are multiplied in pairs, resulting in the number 45. In other words, the numbers that divide 45 exactly are the factors of 45.

45/1 = 45

45 /3 = 15

45/5 = 9

45/9 = 5

45/15 = 3

45/45 = 1

So factors of 45 are 1, 3, 5, 9, 15, 45

The prime factors of 45

divisors | quotient |

3 | 45 |

3 | 15 |

5 | 5 |

1 | |

The divisors are 3, 3, 5 which will then multiply each other = 3 x 3 x 5

So, the prime factorization of 45 = 3 x 3 x 5 = 3^{2} x 5

**56**

The factors of 56 are the numbers multiplied in pairs, resulting in the number 56. In other words, the numbers that divide 56 exactly are the factors of 56.

56/1 = 56

56 /2 = 28

56/4 = 14

56/7= 8

56/8 = 7

56/14 = 4

56/ 28 = 2

56/56 = 1

So factors of 28 are 1, 2, 4, 7, 8, 14, 28, 56

The prime factors of 56

divisors | quotient |

2 | 56 |

2 | 28 |

2 | 14 |

7 | 7 |

1 |

The divisors are 2, 2, 2, 7, which will then multiply each other = 2 x 2 x 2 x 7

So, the prime factorization of 56 = 2 x 2 x 2 x 7 = 2^{3} x 7