Grade 6 Product of Primes Understand the unique

Grade 6 Product of Primes Understand the unique factorisation theorem and perform prime factor decompositions If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Factors Powers Factor trees Unique factorisation theory Prime factor Product of prime factors

How to express a number as a product of prime factors • If a factor of a number is prime number it is a prime factor • All integers > 1 can be written as a product of its prime factors • Can find the prime factors of a number using factor trees • No two numbers have the same prime factor decomposition (The unique factorisation theorem)

How to express a number as a product of prime factors 250 10 25 5 Split the number into two of its factors (not one or itself) 5 5 Keep doing this until you cannot divide a factor any more (when you’ve reached a prime number) 2 Write the prime numbers: 5 x 5 x 5 x 2 We can use powers to simpify: 2 x 5³ This is called the prime factor decomposition

Write the following as a product of its prime factors – now you try. . . a) b) c) d) e) f) g) 280 540 190 500 720 985 1036

Write the following as a product of its prime factors – now you try. . . a) b) c) d) e) f) g) 280 540 190 500 720 985 1036 2³ x 5 x 7 2² x 3³ x 5 2 x 5 x 19 2²x 5³ 2⁴ x 3² x 5 5 x 197 2² x 7 x 37

Use the product of prime factors to work out the original number? • 2² x 3³ x 5⁷ • 2² x 7³ • 5³ x 7² • 13² x 2

Use the product of prime factors to work out the original number? • 2² x 3³ x 5⁷ = 8437500 • 2² x 7³ = 1372 • 5³ x 7² = 6125 • 13² x 2 =338

Problem Solving and Reasoning 2248 has a prime factor decomposition of x³y. Find the value of x and y.

Problem Solving and Reasoning 2248 has a prime factor decomposition of x³y. Find the value of x and y. 2248 2 1124 562 2 2 281 X=2 Y= 281

Reason and explain Can any two numbers have the same prime factor decomposition? Explain why. . . What is wrong with this prime factor decomposition? 4² x 3³ x 7³³ If 48= 2 x 2 x 3 find the prime factor decomposition of 96