# 5th Grade - Prime Factors

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 Grade Level: 5th Skill: Numbers - Small, Large and Prime Topic: Prime Factors Goal: Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2 x 2 x 2 x 3 = 23 x 3). Skill Description: Understanding that a prime number has only two factors, one and itself. Identifying that a composite number has more than two factors. Then, breaking down composite numbers into their prime number products (with exponents)

## Building Blocks/Prerequisites

### Sample Problems

 (1) Define the word "factor" (any number that can be multiplied by to get the original number. 4 is a factor of 12 because it can be multiplied by 3 to equal 12) (2) List 5 prime numbers (3) Why is the number 2 the only even prime number? (all other even numbers are divisible by 2) (4) What are all the factors of 24? Make a factor tree using 2x12 and 6x4. Why do you get the same answer? 24 24 X 4 2 x 12 3x2 2x2 6x2 3x2 2^3 x 3 3^2x2 (5) What does 6 to the 7th power look like written out? 6x6x6x6x6x6x6

### Learning Tips

 (1) Have children practice with relevant numbers in their life deciding whether the number is prime or composite. Use their age, their number of siblings, home address, current date, and other numbers. As an extension, have child explain why a number is composite (example: I am 10 years old, which is a composite number because it is an even number.) This helps them really understand divisibility rules. (2) Children will be able to rule out all even numbers because they are divisible by 2. (3) Any number that ends in a 5 or 0 also is a composite number because it is divisible by 5. (4) Students tend to confuse repeated addition with repeated multiplication. Remind them that repeated addition is multiplication and that repeated multiplication is exponents (5) Testing out how numbers increase exponentially is really fun to do on a calculator. Students can type in a number multiplied by the same number (for example, 9x9) and then continue to press the equals button to watch the calculator multiply exponentially. Calculator “races” can be kind of fun!

### Online Resources

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### Extra Help Problems

 (1) Write the prime factors for the number: 10 (1,2,5,10) (2) Write the prime factors for the number: 25 (1,5,25) (3) Write the prime factors for the number: 12 (1,3,4,2,6,12) (4) Write the prime factors for the number: 32 (1,4,8,32) (5) Write the prime factors for the number: 18 (1,2,3,6,9,18) (6) What does this product look like with exponents? 3x3x3x3 (3^4) (7) What does this product look like with exponents? 9x9x9x9x9 (9^5) (8) What does this product look like with exponents? 217x217 (217^2) (9) What does this product look like with exponents? 8x8x8x8x8x8x8x8x8x8 (8^10) (10) Work backwards – solve this equation to find the composite number 2x2x3 (12) (11) Work backwards – solve this equation to find the composite number 2x2x3x3 (36) (12) Work backwards – solve this equation to find the composite number 2x3x5 (30) (13) Work backwards – solve this equation to find the composite number 3x3x3x3 (81) (14) Write this number out in expanded form 6 to the power of 4 (6x6x6x6) (15) Write this number out in expanded form 8 to the power of 5 (8x8x8x8x8) (16) Write this number out in expanded form 2 to the power of 8 (2x2x2x2x2x2x2x2) (17) Write this number out in expanded form 436 to the power of 3 (436x436x436) (18) Write this number out in expanded form 1999 to the power of 2 (1999x1999)

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