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PLC Papers Created For: Year 11 Topic Practice Paper: Product Of Prime Factors [Type here] Product of prime factors 1 Grade 6 Objective: Understand the unique factorisation theorem and perform prime factor decompositions Question 1 Complete: Every prime number has exactly ________ factors. Those factors are ______ and ________. (1) Question 2 Use this prime factor tree to write 54 as a product of its prime factors 54 6 9 2(1) 3 2 3 3 …………………… (1) PiXL PLC 2017 Certification [Type here] Question 3 Write each of the following number as a product of its prime factors i) 28 …………………… (2) ii) 132 …………………… (3) iii) 225 …………………… (3) Total /10 PiXL PLC 2017 Certification [Type here] Product of prime factors 2 Grade 6 Objective: Understand the unique factorisation theorem and perform prime factor decompositions Question 1 Look at the numbers below 11, 13, 15, 17, 19 a) Which number in the list is not prime ……………………….. b) Explain why it is not prime. ………………………………………………………………………………………………… ………………………………………………………………………………………………… (2) Question 2 Write each of the following number as a product of its prime factors i) 44 …………………… (2) ii) 325 …………………… (3) PiXL PLC 2017 Certification [Type here] iii) 840 …………………… (3) Total /10 PiXL PLC 2017 Certification Product of prime factors 3 Grade 6 Objective: Understand the unique factorisation theorem and perform prime factor decompositions Question 1 Given A = 22 x 35 x 53 and B = 24 x 33 x 52 Write down, as a product of its prime factors, a) The highest common factor of A and B ………………… (1) b) The lowest common multiple of A and B ………………… (1) Question 2 a) Express 24 as a product of its prime factors ………………… (2) b) Use your answer to write 482 as a product of its prime factors in index form ………………… (2) PiXL PLC 2017 Certification Question 3 A number, n, in prime factor form is 32x3y, where x and y are odd prime numbers. a) Circle the expressions which are factors of n 18 3xy x4y x2 9y b) Circle the expressions which are multiples of n 18x3y 3xy 9x3y2 x3y 81x3y (4) Total /10 PiXL PLC 2017 Certification Product of prime factors 4 Grade 6 Objective: Understand the unique factorisation theorem and perform prime factor decompositions Question 1 a) Express 40 as a product of its prime factors ………………… (2) b) Use your answer in part a) to write the following numbers as a product of prime factors i) 120 …………………… (1) ii) 240 …………………… (1) iii) 360 …………………… (1) PiXL PLC 2017 Certification Question 2 Leela and Gabriel both write 6300 as a product of its prime factors. Leela writes 6300 = 22 x 32 x 52 x 7 Gabriel writes 6300 = 2 x 33 x 5 x 7 Who is correct? Explain why. …………………………………………………………………………………………………. ………………………………………………………………………………………………….. (2) Question 3 p, q and r are prime numbers such that pq2r3 = 540. Work out the value of p, q and r. …………………… (3) Total /10 PiXL PLC 2017 Certification PLC Papers Created For: Year 11 Topic Practice Paper: Product Of Prime Factors [Type here] Product of prime factors 1 Grade 6 Solutions Objective: Understand the unique factorisation theorem and perform prime factor decompositions Question 1 Complete: Every prime number has exactly two factors. Those factors are one and itself. C1 for all three (1) Question 2 Use this prime factor tree to write 54 as a product of its prime factors 54 6 9 2(1) 3 2 3 3 2 x 3 x 3 x 3 (B1) …………………… (1) Question 3 Write each of the following number as a product of its prime factors i) 28 M1 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error A1 for 2 x 2 x 7 …………………… (2) PiXL PLC 2017 Certification [Type here] ii) 132 M2 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error (M1 for 132 written as a correct product with only one non-prime or equivalent division or a full process with 2 calculation errors.) A1 for 2 x 2 x 3 x 11 …………………… (3) iii) 225 M2 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error (M1 for 225 written as a correct product with only one non-prime or equivalent division or a full process with 2 calculation errors.) A1 for 3 x 3 x 5 x 5 …………………… (3) Total /10 PiXL PLC 2017 Certification [Type here] Product of prime factors 2 Grade 6 Solutions Objective: Understand the unique factorisation theorem and perform prime factor decompositions Question 1 Look at the numbers below 11, 13, 15, 17, 19 a) Which number in the list is not prime ……………15………….. b) Explain why it is not prime. 15 has factors other than 1 and itself, such as 5 and 3 (C1) (2) Question 2 Write each of the following number as a product of its prime factors i) 44 M1 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error A1 for 2 x 2 x 11 …………………… (2) ii) 325 M2 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error (M1 for 325 written as a correct product with only one non-prime or equivalent division or a full process with 2 calculation errors.) A1 for 5 x 5 x 13 …………………… (3) PiXL PLC 2017 Certification [Type here] iii) 840 M2 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error (M1 for 840 written as a correct product with only one non-prime or equivalent division or a full process with 2 calculation errors.) A1 for 2 x 2 x 2 x 3 x 5 x 7 …………………… (3) Total /10 PiXL PLC 2017 Certification Product of prime factors 3 Grade 6 Solutions Objective: Understand the unique factorisation theorem and perform prime factor decompositions Question 1 Given A = 22 x 35 x 53 and B = 24 x 33 x 52 Write down, as a product of its prime factors, a) The highest common factor of A and B ……22 x 33 x 52 (A1)…………… (1) b) The lowest common multiple of A and B ……24 x 35 x 53 (A1)…………… (1) Question 2 a) Express 24 as a product of its prime factors M1 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error A1 for 2 x 2 x 2 x 3 ………………… (2) b) Use your answer to write 482 as a product of its prime factors in index form ((2 x 2 x 2 x 3) x2 )2 (M1- allow ft marks) 28 x 32 (A1) ………………… (2) PiXL PLC 2017 Certification Question 3 A number, n, in prime factor form is 32x3y, where x and y are odd prime numbers. a) Circle the expressions which are factors of n 18 3xy x4y x2 9y A2 for all three correct, no errors (M1 for any two correct, allow one error) b) Circle the expressions which are multiples of n 18x3y 3xy 9x3y2 x3y 81x3y A2 for all three correct, no errors (M1 for any two correct, allow one error) (4) Total /10 PiXL PLC 2017 Certification Product of prime factors 4 Grade 6 Solutions Objective: Understand the unique factorisation theorem and perform prime factor decompositions Question 1 a) Express 40 as a product of its prime factors M1 for full systematic method of divisions by prime numbers oe factor trees; condone 1 calculation error A1 for 2 x 2 x 2 x 5 ………………… (2) b) Use your answer in part a) to write the following numbers as a product of prime factors i) 120 B1 for (2 x 2 x 2 x 5) x 3 (allow ft marks) …………………… (1) ii) 240 B1 for (2 x 2 x 2 x 5) x 3 x 2 (allow ft marks) …………………… (1) iii) 360 B1 for (2 x 2 x 2 x 5) x 3 x 3 (allow ft marks) …………………… (1) PiXL PLC 2017 Certification Question 2 Leela and Gabriel both write 6300 as a product of its prime factors. Leela writes 6300 = 22 x 32 x 52 x 7 Gabriel writes 6300 = 2 x 33 x 5 x 7 Who is correct? Explain why. Prime factor tree drawn or multiplication of prime factors to establish correct answer (M1) Leela (A1) dependant on M1 (2) Question 3 p, q and r are prime numbers such that pq2r3 = 540. Work out the value of p, q and r. M1 for full systematic method of at least 4 divisions by prime numbers oe factor trees; condone 1 calculation error A1 for 2 x 2 x 3 x 3 x 3 x 5 B1 for p = 5, q = 2 and r = 3 …………………… (3) Total /10 PiXL PLC 2017 Certification