1. Factors & Number Theory
Grade 6
Copyright © Ed2Net Learning, Inc.

2. Copyright © Ed2Net Learning, Inc.
Factors
A whole number that divides exactly into another whole number is called a factor of that number.
For example: 100 / 25 = 4
So, 25 is a factor of 100 as it divides exactly into 20.
20 / 4 = 5
So, 4 is a factor of 20 as it divides exactly into 20.
Copyright © Ed2Net Learning, Inc.

3. How do we check if a number is a factor of another number
We divide 22 by 7 and check if remainder is zero 3
7 ) 22 21 1
As the remainder is 1 we conclude that 7 is not
a factor of 22.
Copyright © Ed2Net Learning, Inc.

4. Copyright © Ed2Net Learning, Inc.
Try This!
Find the factors of 20
List all the factors of 35.
Copyright © Ed2Net Learning, Inc.

5. Copyright © Ed2Net Learning, Inc.
Powers and Exponents
Exponent 46
Base
The exponent is sometimes referred to as the power.
Copyright © Ed2Net Learning, Inc.

6. Copyright © Ed2Net Learning, Inc.
46 means to multiply the base 4 by itself 6 times
46 = 4 x 4 x 4 x 4 x 4 x 4
However we must remember that
40 = 1
Copyright © Ed2Net Learning, Inc.

7. Copyright © Ed2Net Learning, Inc.
Try This!
3 x3 + 5 y2 =
3.5x2 y3 - xy2 =
Where x = (-2) and y = (-3)
Copyright © Ed2Net Learning, Inc.

8. Copyright © Ed2Net Learning, Inc.
Prime Numbers
A Prime number is a positive integer >1
A number that has exactly two factors, 1 and itself
A number that cannot be factored .
7 is a Prime number as it has only two factors 1 and 7
Copyright © Ed2Net Learning, Inc.

9. Copyright © Ed2Net Learning, Inc.
Composite Numbers
When a whole number greater than one has more than 2 factors it is called a Composite Number.
10 is a composite number as it has 1, 2, 5 and 10 as its factors
Copyright © Ed2Net Learning, Inc.

10. Copyright © Ed2Net Learning, Inc.
Prime Factorization
Expressing a composite number as a product of prime numbers is called Prime Factorization
The number 60 is a composite number. It can be written as the product 2 x 2 x 3 x 5. Note that 2, 3 and 5 are factors of 60 and all these factors are prime numbers. We call them prime factors.
When we express a number as a product of prime factors, we have actually factored it completely. We refer to this process as
prime factorization
Copyright © Ed2Net Learning, Inc.

11. Methods for finding Prime Factorization
460 *
2 * * 2
460 = 2 * 2 * 5 * 23
Prime factors of 460 are
2² * 5 * 23
Copyright © Ed2Net Learning, Inc.

12. Copyright © Ed2Net Learning, Inc.
Try This!
Find out the Prime Factors of the following
56 =
24 =
Copyright © Ed2Net Learning, Inc.

13. Greatest Common Factor
Greatest Common Factor of two or more numbers can be defined as the greatest number that is a factor of each number
Copyright © Ed2Net Learning, Inc.

14. Greatest Common Factor
Method 1:
List the factors of each number. Then identify the common factors. The greatest of these common factors is the GCF.
Method 2:
Write the prime factorization of each number. Then identify all common prime factors and find their product.
Copyright © Ed2Net Learning, Inc.

15. Greatest Common Factor
Find the GCF of 27 and 36
Method 1:
List all the factors of both the numbers
Factors of 27 : 1, 3, 9, 27
Factors of 36 : 1, 2, 3, 4, 6, 9, 12, 18, 36
Thus, the GCF of 27 and 36 is 9
Copyright © Ed2Net Learning, Inc.

16. Greatest Common Factor
Method 2
Write the prime factorization of 27 and 36
3 x x
x x 4
x 2
Common Prime factors are 3 x 3 = 9
Copyright © Ed2Net Learning, Inc.

17. Copyright © Ed2Net Learning, Inc.
Try This!
Find GCF of the following set of numbers
160 and 550
2) 20a2 and 14ab
3) 36, 24, 144, 96
Copyright © Ed2Net Learning, Inc.

18. Copyright © Ed2Net Learning, Inc.
Lets take a Break !
Copyright © Ed2Net Learning, Inc.

19. Copyright © Ed2Net Learning, Inc.

20. Copyright © Ed2Net Learning, Inc.
Least Common Multiple
The least common multiple of the numbers a and b is the smallest number that is divisible by both a and b.
We denote the least common multiple of a and b by LCM (a, b).
Copyright © Ed2Net Learning, Inc.

21. Copyright © Ed2Net Learning, Inc.
Method 1
List several multiples of each number. Then identify the common multiples. The least of these is the LCM.
Multiples of 6 : 6, 12, 18, 24, 30,36,…
Multiples of 9 : 9, 18, 27, 36, 45, 54, 63,...
As 18 is the least number which is a common multiple hence
LCM of 6 and 9 is 18
Copyright © Ed2Net Learning, Inc.

22. Copyright © Ed2Net Learning, Inc.
Method 2
Find the prime factors of each number, then identify all common prime factors. For each prime factor, write it down the greatest number of times it appears in any of the numbers. The product is the LCM
9 = 3 x 3 = 32
12 = 2 x 2 x 3 = 22 x 3
15 = 3 x 5
Copyright © Ed2Net Learning, Inc.

23. Copyright © Ed2Net Learning, Inc.
The prime factors are 2, 3 and 5. The greatest number of times 2 appears is twice (in 12), So we write it down twice. The greatest number of times 3 appears is twice (in 9), so we again write it down twice. The greatest number of times 5 appears is once (in 15), so write it down once. The LCM of 9, 12 and 15 is
2 x 2 x 3 x 3 x 5 = 180
Copyright © Ed2Net Learning, Inc.

24. Copyright © Ed2Net Learning, Inc.
Try This!
Find the LCM of the following
1) 56 and 16
2) 3, 7, 14
3) 29, 58, 4
Copyright © Ed2Net Learning, Inc.

25. Copyright © Ed2Net Learning, Inc.
Express the smallest five digit number in the form of prime numbers 1)
Copyright © Ed2Net Learning, Inc.

26. Copyright © Ed2Net Learning, Inc.
2) Diana is thinking of two numbers The GCF is 6 and the LCM is 36. If one of the number is 12, what is the other number?
Copyright © Ed2Net Learning, Inc.

27. Copyright © Ed2Net Learning, Inc.
3) The product of any three consecutive numbers is always divisible by 6. Comment.
Copyright © Ed2Net Learning, Inc.

28. Copyright © Ed2Net Learning, Inc.
Great Job Done!
Be sure to practice what you have learned today!!!
Copyright © Ed2Net Learning, Inc.