PRIME FACTORIZATION WORKSHEET

Write the Prime Factorization of the Number

Write the prime factorization of the number:

1)  26     Solution

2)  58    Solution

3)  63    Solution

4)  85   Solution

5)  120   Solution

6)  160    Solution

7)  154    Solution

8)  195    Solution

9)  225   Solution

10)  210    Solution

Problem 11 :

What is the greatest perfect square that is a factor of 1575?

Solution

Problem 12 :

What is the greatest perfect square that is a factor of 396? Explain

Solution

Problem 13 :

Describe and correct the error in writing the prime factorization.

Solution

Problem 14 :

Find the number represented by the prime factorization.

a)  2² ⋅ 3² ⋅ 5

b)  3² ⋅ 5² ⋅ 7

c)  2³ ⋅ 11² ⋅ 13

Solution

Problem 15 :

Find the greatest perfect square that is a factor of the number.

a)  244

b)  650

c)  756

d)  1290

Solution

Problem 15 :

The coach of a baseball team separates the players into groups for drills. Each group has the same number of players. Is the total number of players on the baseball team prime or composite? Explain

Solution

Prime Factorization Method to Find HCF and LCM

Find the HCF of LCM of following numbers using prime factorization method :

1)  9, 12    Solution

2)  8, 16   Solution

3)  18, 42   Solution

4)  14, 42   Solution

5)  18, 30   Solution

6)  24, 32   Solution

7)  12, 36    Solution

8)  15, 33    Solution

9)  72, 96   Solution

10)  108, 144   Solution

11)  78, 130   Solution

Problem 12 :

The brass section of a marching band has 30 members. The band director arranges the brass section in rows. Each row has the same number of members. How many possible arrangements are there?

Solution

Problem 13 :

You are filling piñatas for your sister’s birthday party. The list shows the gifts you are putting into the piñatas. You want identical groups of gifts in each piñata with no gifts left over. What is the greatest number of piñatas you can make?

Solution

Write the prime factorization of the number:

Problem 1 :

20

Solution

Problem 2 :

72

Solution

Problem 3 :

68

Solution

Problem 4 :

55

Solution

Problem 5 :

30

Solution

Problem 6 :

74

Solution

Problem 7 :

105

Solution

Problem 8 :

108

Solution

Problem 9 :

90

Solution

Problem 10 :

198

Solution

Problem 11 :

Which number is a prime factor of 572?

a) 4     b) 7      c) 13      d)  22

Solution

Problem 12 :

What is the prime factorization of 1100?

Solution

Problem 13 :

Which of the following is pair of co-primes? 

a)  (16, 62)     b) (18, 25)    c)  (21, 35)     d)  (23, 92)

Solution

Problem 14 :

The greatest number of four digits which is divisible by 15, 25, 40 and 75.

a)  9000     b) 9400    c)  9600     d)  9800

Solution

Problem 15 :

The least number should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is 

a)  3         b) 13       c)  23       d)  33

Solution