Prime Factorisation

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Simon Thomas

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Simon Thomas 5 years, 1 month ago

Published this.

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Simon Thomas 5 years, 1 month ago

Created this as a copy of LCM and HCF.

Name	Status	Author	Last Modified
LCM and HCF	draft	Simon Thomas	16/03/2020 13:42
Prime Factorisation	draft	Simon Thomas	16/03/2020 13:42
NB4 - HCF	Ready to use	Andrew Neate	10/04/2024 09:14
NB5 - LCM	Ready to use	Andrew Neate	10/04/2024 09:15
NG1 Simplify (cancel down) Fractions	Ready to use	Andrew Neate	10/04/2024 09:35
Merryn's copy of LCM and HCF	Ready to use	Merryn Horrocks	07/03/2024 01:07

There are 7 other versions that do you not have access to.

Question statement

In each of these questions, write the given number as a product of powers of primes in ascending order.

Give your answer in list form, where

the 1st element represents the power of 2

the 2nd element represents the power of 3

the 3rd element represents the power of 5

the 4th element represents the power of 7

For example

$210=2\times3\times5\times7$ we would give our answer as $[1,1,1,1]$

$63=3^2\times7$ we would give our answer as $[0,2,0,1]$

$750=2\times3\times5^3$ we would give our answer as $[1,1,3,0]$

Give any introductory information the student needs.

			Name	Type	Generated Value

x_powers	list	[ 2, 4, 0, 1 ]
y_powers	list	[ 0, 2, 0, 2 ]
z_powers	list	[ 1, 2, 1, 1 ]
x	number	2268
y	number	441
z	number	630
primes	list	List of 15 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[random(1..4),random(0..4),random(0..3),random(1..3)]

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 2, 4, 0, 1 ]

→ Used by:

Variable testing condition

Advice

To find the prime factorisation of a number, keep breaking that number down into pairs of factors until all number written down are primes.

e.g. To find the prime factorisation of $2450$ we could note that

$2450 = 245 \times 10$

$2450=245 \times \underline{5} \times \underline{2}$

$2450=\underline{5} \times 49 \times \underline{5}\times \underline{2}$

$2450=\underline{5} \times \underline{7} \times \underline{7} \times \underline{5} \times \underline{2}$

where we have underlined the primes as we go along.

Rewriting this in ascending order of primes, we obtain $2450 = 2 \times 5 \times 5 \times 7 \times 7$

which we can also write as $2450 = 2 \times 5^2 \times 7^2$

(a) Applying a similar method to the given questions, we can obtain:

We can write the given numbers as products of prime factors as follows:

$\var{x}=\var{show_factors(x)}$

$\var{y}=\var{show_factors(y)}$

$\var{z}=\var{show_factors(z)}$

Give a worked solution to the whole question.

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This question is used in the following exams:

Working with Prime Factorisation by Simon Thomas in Maths support.
Prime Factorisation by Chris Templet in Chris's workspace.
CMPU1018_CA1 by Blathnaid Sheridan in Blathnaid's workspace.
CMPU1018 Number Theory Quiz 1 by Blathnaid Sheridan in Blathnaid's workspace.

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Taxonomy: mathcentre

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Simon Thomas 5 years, 1 month ago

Simon Thomas 5 years, 1 month ago

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Generated value: `list`

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Prime Factorisation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 5 years, 1 month ago

Simon Thomas 5 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `list`