Mada za sehemu hiiUse ordering skills to solve puzzles in everyday lifeMada 8
- Identify even, odd and prime numbers
- Calculate factors and multiples of numbers not exceeding three digits
- Calculate the Lowest Common Multiple (LCM) and Greatest Common Factor (GCF) of whole numbers
- Addition and subtraction of fractions with different denominators
- Addition and subtraction of mixed fractions
- Multiplication of decimals
- Divide numbers to obtain an answer with no more than three decimal places
- Convert percentages into fractions and decimals
Finding the GCF and LCM of Whole Numbers
When we work with two or more numbers, we often need to find numbers that they share. The Greatest Common Factor (GCF) is the largest number that divides into two or more numbers without leaving a remainder. The Lowest Common Multiple (LCM) is the smallest number that two or more numbers can divide into without leaving a remainder. These skills help us in everyday situations like sharing items equally or grouping things.
The GCF tells us the biggest number that can divide into two or more numbers at the same time.
Method 1: Listing All Factors
Step 1: List all factors of each number. Step 2: Find the common factors (factors that appear in both lists). Step 3: The greatest of these common factors is the GCF.
Example: Find the GCF of 30 and 42.
Solution:
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Common factors: 1, 2, 3, 6
- Greatest common factor: 6
So, the GCF of 30 and 42 is 6.
Method 2: Using Prime Factors
Step 1: Write each number as a product of prime factors. Step 2: Find the common prime factors. Step 3: Multiply these common prime factors together.
Example: Find the GCF of 12 and 18 using prime factors.
Solution:
- Prime factors of 12: 2 × 2 × 3
- Prime factors of 18: 2 × 3 × 3
- Common prime factors: 2 and 3
- Multiply them: 2 × 3 = 6
So, the GCF of 12 and 18 is 6.
The LCM tells us the smallest number that two or more numbers can divide into evenly.
Method 1: Listing Multiples
Step 1: Write the multiples of each number. Step 2: Find the common multiples (multiples that appear in both lists). Step 3: The smallest of these common multiples is the LCM.
Example: Find the LCM of 3 and 4.
Solution:
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...
- Common multiples: 12, 24, ...
- Lowest common multiple: 12
So, the LCM of 3 and 4 is 12.
Method 2: Using Prime Factors
Step 1: Write each number as a product of prime factors. Step 2: Take each prime factor the greatest number of times it appears in any one number. Step 3: Multiply these together.
Example: Find the LCM of 12 and 20.
Solution:
| 12 | 20 | |
|---|---|---|
| 2 | 6 | 10 |
| 2 | 3 | 5 |
| 3 | 3 | 5 |
| 5 | 1 | 5 |
- Prime factors to use: 2, 2, 3, 5
- Multiply: 2 × 2 × 3 × 5 = 60
So, the LCM of 12 and 20 is 60.
- GCF = Greatest Common Factor → the biggest number that divides into both
- LCM = Lowest Common Multiple → the smallest number that both divide into
- Use listing method when numbers are small
- Use prime factors method when numbers are larger
In Tanzanian daily life, GCF and LCM are very useful. For example, when a market vendor has 30 oranges and 45 bananas and wants to make identical fruit baskets using all the fruits with no leftovers, the GCF helps determine the greatest number of baskets they can make (the GCF of 30 and 45 is 15 baskets). Similarly, if two buses leave the same station — one every 12 minutes and another every 18 minutes — the LCM tells us after how many minutes they will leave together again (the LCM of 12 and 18 is 36 minutes).
Swali
What is the Greatest Common Factor (GCF) of two or more numbers?
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