Prime Factorization Lesson Plan Pdf

Prime Factorization

This is a complete lesson with didactics and exercises almost prime number factorization, meant for 4th or 5th form. It first briefly reviews what are primes, so explains how to factor numbers using a factor tree. Afterward several examples, there are many factorization exercises for the students.

Then the lesson explains how all numbers are "built" from primes, and includes exercises about that process.

Some numbers merely have two divisors: 1 and the number itself. Such numbers are called prime numbers. 11 is one of them.		factor		factor		product
		1	×	11	=	11

In the last lesson, nosotros found that the prime numbers less than 30 are 2, 3, 5, vii, eleven, 13, 17, 19, 23, and 29. One is commonly not counted as a prime number.

Prime factorization using a factor tree

A factor tree is a handy way to factor numbers to their prime factors. The factor tree starts at the root and grows upside down!

We want to factor 24 and so we write 24 on top. Commencement, 24 is factored into four × 6. However, 4 and 6 are non primes, so we can continue factoring. Four is factored into 2 × ii and six is factored into 2 × iii.

Nosotros will not gene 2 or 3 whatsoever farther because they are prime numbers.

(root)		24
/ \
	4	×	vi
	/ \		/ \
(leaves)	2 × 2	×	two × 3

Once you go to the primes in your "tree", they are the "leaves", and y'all end factoring in that "branch". And so 24 = two × 2 × ii × 3. This is the prime factorization of 24.

Examples:

thirty

/ \

5 × 6

/ \

two × iii

five is a prime number—it is a "foliage". Once done, "pick the leaves"—you lot can even circle them to come across them better! So, xxx = two × 3 × 5.

Both iii and 7 are prime number numbers, and then nosotros cannot factor them whatsoever further.
So 21 = 3 × 7.

/ \

11 × vi

/ \

2 × 3

/ \

2 × 33

/ \

xi × 3

You lot can start the factoring process any way you want. The terminate result is the same: 66 = 2 × three × 11.

/ \

12 × 6

/ \ / \

3 × 4 × 2 × 3

/ \

2 × 2

72 has lots of factors then the factoring takes many steps.

72 = 2 × 2 × 2 × iii × three

Nosotros could take also started by writing 72 = ii × 36 or 72 = 4 ×18.

How can you get started?
Check:
- is 57 in whatsoever of the
times tables?
- is it divisible by two?
By iii? By 5?

How tin yous go started?
Cheque:
- is 65 in whatever of the
times tables?
- is it divisible by ii?
By 3? By v?

ane. Factor the post-obit numbers to their prime factors.

a. 18 / \	b. 6 / \	c. fourteen / \
d. eight / \	e. 12 / \	f. 20 / \
yard. xvi / \	h. 24 / \	i. 27 / \
j. 25 / \	grand. 33 / \	l. fifteen / \

2. Factor the post-obit numbers to their prime factors.

a. 42 / \	b. 56 / \	c. 68 / \
d. 75 / \	due east. 47 / \	f. 99 / \
g. 72 / \	h. 80 / \	i. 97 / \
j. 85 / \	k. 66 / \	l. 82 / \

Prime numbers are similar edifice blocks of all numbers. They are the first and foremost, and other numbers are "built" from them. "Edifice numbers" is like factoring backwards. We beginning with the building blocks—the primes—and see what number we go:

ii × v	×	2 × 2
\ / \ /
x	×	four
\ /
	40

2 × 3	×	ii × 3	×	2
\ /		\ /		\|
half-dozen	×	6	×	2
\|		\ /
vi	×	12
\ /
72

5 × 2	×	vii
\ / \|
10	×	7
\ /
70

2 × 7	×	ii	×	3
\ /		\ /
14	×	6
\ /
84

Past using the procedure higher up (building numbers starting from primes) you lot can build Whatever whole number there is! Tin you believe that?

We can say this in another mode: ALL numbers tin can exist factored then the factors are prime numbers. That is sort of astonishing! This fact is known as the fundamental theorem of arithmetic. Indeed, it is central.

992
/ \
4 × 248
/ \ / \
ii × 2	× 4 × 62
	/ \ / \
	ii × 2 × 2 × 31

So, no affair what the number is—992 or 83,283 or 150,282—it can be written as a production of primes.

Meet 992 factored on the right. 992 = 2 × 2 × 2 × 2 × two × 31. For 83,283 we become three × 17 × 23 × 71, and 151,282 = 2 × 3 × iii × 3 × 11 × 11 × 23.

To notice these factorizations, y'all demand to test-divide the numbers past various primes so it is a chip deadening. Of course, computers can do the divisions very quickly.

3. Build numbers from primes.

a. 2 × five × 11 \ / \|	b. 3 × 2 × two × 2 \ / \ /	c. two × 3 × 7 \ / \|
d. 11 × 3 × 2 \| \ /	e. 3 × 3 × 2 × 5 \ / \ /	f. 2 × 3 × 17

iv. Build more than numbers from primes.

a. 2 × 5 × 13

b. 7 × thirteen × two × 11

c. nineteen × 3 × v × 2

5. Try it on your own! Pick 3-6 primes every bit you wish (you lot can use the same prime
several times), and see what number is built from them.

Ready for a challenge? Use your cognition of divisibility tests and the figurer, and find the prime factorization of these numbers:
a. ii,145	b. 3,680	c. 10,164