Download Product Of Prime Factors

PLC Papers
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Year 11 Topic Practice Paper: Product Of Prime Factors
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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)
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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
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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)
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iii)
840
……………………
(3)
Total /10
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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)
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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
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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)
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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
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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
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)
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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
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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)
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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
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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)
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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
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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)
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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
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