For the last few months, I’ve been working on study materials on exponents and roots. While doing research for the packet, I started to get interested in factors and especially prime factors. It turns out that they are really useful for thinking about lots of different kinds of math that we have been looking recently. For example, the mathematics of bicycle gears or Spirograph both have to do with factors, as do fractions, place value, exponents and other math that is relevant to math teaching in adult literacy.
In this meeting, Mark started us off by sharing an image from the board game Prime Climb, a game designed by mathematicians from the organization Math for Love. (Their other game, Tiny Polka Dots, is fantastic for kids 3 and up.)
Take a minute looking at these numbers on your own…
…
Can you predict what 30 would look like?…
…
The group noticed that orange represents 2, green represents 3 and blue represents 5. We also noticed a relationship that all the multiples of 2 have an orange section and all multiples of 5 have a blue section. We discussed other patterns the group noticed and shared questions, then looked at the numbers 1-60 in this visual representation.
Look at the number 30.
Orange means 2. Green means 3. Blue means 5.
If we think of these numbers as factors, we see that 2 x 3 x 5 = 30.
It turns out that these three numbers are the prime factors of 30. There are other factors (1, 6, 15, 10 and 30), but those numbers aren’t prime. The prime factors are special because they can be used to represent the number. 2x3x5 (or 2x5x3, 3x2x5, etc.) all equal 30.
The group then played the game Prime Climb and moved on to stations with the following problems and materials:
- The Power of Exponents (section on Factors, Multiples and Prime Factorization)
- Greatest Common Factors and Least Common Multiples (thanks, @benjamindickman )
- Terminating and Non-Terminating Decimals (thanks, @socker8711)
We spent the last few minutes of the meeting looking at the overlapping prime factors of two numbers and considering what this represents.
What is 5×3 in relation to 30 and 45?
We then considered this question as a group:
The greatest common factor of two numbers is 12 and the least common multiple of the same two numbers is 360. What are the two numbers?
In Attendance: Alisa, Andrew, Brigette, Deneise, Eric, Mark, and Nadia
Programs Represented: Brooklyn Public Library, CUNY LINCT, CUNY Adult Literacy PD team
Respectfully submitted by Eric.
I have figured a matrix of counting numbers that contain prime numbers in a very discernable, repetitive pattern. I would enjoy sharing this with your community.
I have found some interesting fact in factorizing Prime no. I don’t know whether someone has already discovered it or not. I have searched Google but haven’t find anyone using this method.
If we have the sum and product of the two Prime numbers it is very easy to find the two numbers. I have searched the solution for this equation but everyone is using Quadratic equation to solve it.
But there is a very simple was to solve it.
Let P and Q be 2 Prime number
N = product of P and Q
M = Sum of P and Q
A = M divided by 2
So to find P and Q
We will first square A and then minus it from N and the result will always be a perfect square lets note it as B square
So A square – N = B square
P = A – B
Q = A + B
Example 1
N = 91 (Product of P and Q)
M = 20 (Sum of P and Q)
A = 10 (M/2)
As per the formula
A square – N = B square
10 square – 91 = B square
100 – 91 = 9
B square = 9
B = 3
P = A – B
= 10 – 3
= 7
Q = A + B
= 10 + 3
= 13