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Specific Objectives
By the end of the topic the learner should be able to:
The learner should be able to test the divisibility of numbers by 2, 3, 4, 5, 6, 8, 9, 10 and 11.
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Content
Divisibility test of numbers by 2, 3, 4, 5, 6, 8, 9, 10 and 11
Introduction
Divisibility test makes computation on numbers easier. The following is a table for divisibility test.
Divisibility Tests | Example |
A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8. | 168 is divisible by 2 since the last digit is 8. |
A number is divisible by 3 if the sum of the digits is divisible by 3. | 168 is divisible by 3 since the sum of the digits is 15 (1+6+8=15), and 15 is divisible by 3. |
A number is divisible by 4 if the number formed by the last two digits is divisible by 4. | 316 is divisible by 4 since 16 is divisible by 4. |
A number is divisible by 5 if the last digit is either 0 or 5. | 195 is divisible by 5 since the last digit is 5. |
A number is divisible by 6 if it is divisible by 2 AND it is divisible by 3. | 168 is divisible by 6 since it is divisible by 2 AND it is divisible by 3. |
A number is divisible by 8 if the number formed by the last three digits is divisible by 8. | 7,120 is divisible by 8 since 120 is divisible by 8. |
A number is divisible by 9 if the sum of the digits is divisible by 9. | 549 is divisible by 9 since the sum of the digits is 18 (5+4+9=18), and 18 is divisible by 9. |
A number is divisible by 10 if the last digit is 0. | 1,470 is divisible by 10 since the last digit is 0. |
A number is divisible by 11 if the sum of its digits in the odd positons like 1st ,3rd ,5th ,7th Positions, and the sum of its digits in the even position like 2nd , 4th ,6th ,8th positions are equal or differ by 11,or by a multiple of 11 | 8,260,439 sum of 8 +6 +4 +9 =27: 2 + 0 +3 = 5 27 – 5 = 22 which is a multiple of 11 |
End of topic
Did you understand everything? If not ask a teacher, friends or anybody and make sure you understand before going to sleep! |
Past KCSE Questions on the topic
CHAPTER FOUR
Specific Objectives
By the end of the topic the learner should be able to:
- Find the GCD/HCF of a set of numbers.
- Apply GCD to real life situations.
Content
- GCD of a set of numbers
- Application of GCD/HCF to real life situations
Introduction
A Greatest Common Divisor is the largest number that is a factor of two or more numbers.
When looking for the Greatest Common Factor, you are only looking for the COMMON factors contained in both numbers. To find the G.C.D of two or more numbers, you first list the factors of the given numbers, identify common factors and state the greatest among them.
The G.C.D can also be obtained by first expressing each number as a product of its prime factors. The factors which are common are determined and their product obtained.
Example
Find the Greatest Common Factor/GCD for 36 and 54 is 18.
Solution
The prime factorization for 36 is 2 x 2 x 3 x 3.
The prime factorization for 54 is 2 x 3 x 3 x 3.
They both have in common the factors 2, 3, 3 and their product is 18.
That is why the greatest common factor for 36 and 54 is 18.
Example
Find the G.C.D of 72, 96, and 300
Solution
72 | 96 | 300 | |
2 | 36 | 48 | 150 |
2 | 18 | 24 | 75 |
3 | 6 | 8 | 25 |
End of topic
Did you understand everything? If not ask a teacher, friends or anybody and make sure you understand before going to sleep! |
Past KCSE Questions on the topic
- Find the greatest common divisor of the term. 144x3y2 and 81xy4
b) Hence factorize completely this expression 144x3y2-81xy4 (2 marks)
