Prime Factorization
Write 5 examples of prime numbers and 5 examples of composite numbers.
Answers will vary :)
List all of the common factors of 32 and 40.
1, 2, 4, 8
Find the LCM of 8 and 20.
40
What is the square of eight?
64
22+4x62-33
121
Use prime factorization to write 70 as a product of its prime numbers.
2 x 5 x 7
Find the GCF of 27 and 63.
9
Find the LCM of 16 and 20.
80
What is the cube of 8?
512
7 x 33-22+43
228
Using prime factorization, write 84 as a product of its prime factors.
84 = 2 x 2 x 3 x 7
What is the greatest common factor of 48, 72, and 112?
16
Find the LCM of 12 and 40.
120
What is the square of 13?
169
Mr. Shaz says that 42+53 x 32 is 2169. He explains that to find the answer, he first adds 42 and 53. Then, he multiplies the sum by 32. Using precise mathematical vocabulary, explain why Mr. Shaz's reasoning is incorrect.
Mr. Shaz's reasoning is incorrect because he did not follow order of operations/GEMDAS. He added before multiplying, when he should've done the opposite.
Is 1 a prime number? Explain why or why not using precise mathematical vocabulary.
No because a prime number has exactly 2 factors (1 and itself) and 1 has only one factor (1).
Find the GCF of 36, 54, and 72.
18
What is the least common multiple of 6, 9, and 12?
36
What is the cube of seven?
343
What is the value of 43+62-52?
75
The number 3720 is 2x2x2x3x5x31 when written as a product of its prime factors. What is the number 372 when written as a product of its prime factors? Using mathematical vocabulary, explain the steps you used to work out the answer.
2x2x3x31
I know that 3720 divided by ten gives me 372, and the prime factorization of ten is two times five, so since I am dividing by ten, I must cancel out the two factors of 2 and 5 from the prime factorization of 3720.
There are 16 girls and 12 boys in Ms. Curry’s 7th grade English class. She would like to make groups in which the boys and girls are evenly distributed to each group. What is the greatest number of groups she can create? How many boys and how many girls are in each group?
4 groups with 4 girls and 3 boys in each
Ms. C needs to buy some candy for her students. Jolly ranchers are sold in packs of 20. Dum Dums are sold in packs of 45. Ms. C wants to buy the same number of each item. What is the least number of packs of each item that she must buy? Justify your answer with precise mathematical vocabulary.
9 packs of Jolly Ranchers and 4 packs of Dum Dums because 180 is the LCM of the 2 numbers, and 9x20=180 and 4x45=180
Write an expression to represent the different between the cube of 16 and the square of 12.
163-122
What is the value of 113+2x82? Using mathematical vocabulary, explain the steps you used to work out your answer.
3635
1. Evaluate all exponents
2. Multiply 36 and 64
3. Add 1331 and 2304 to get 3635