How do you find GCF (boomerang method)?
To find the Greatest Common Factor (GCF) using the boomerang method, follow these steps:
Step 1: List the factors of each given number.
Start by listing all the factors of the two numbers you want to find the GCF for. A factor is a number that divides another number without leaving a remainder.
Step 2: Identify the common factors.
Compare the factors of both numbers and identify the factors they have in common. These common factors will be the ones that divide both numbers without leaving a remainder.
Step 3: Choose the highest common factor.
Out of the common factors, choose the largest one. This largest common factor is the GCF of the two given numbers.
Step 4: Check if the GCF is correct.
To verify that you have correctly identified the GCF using the boomerang method, ensure that the GCF divides both original numbers without leaving a remainder. If it does, then you have found the GCF correctly.
Let's go through an example:
Find the GCF of 36 and 48 using the boomerang method.
Step 1: List the factors of each given number.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Step 2: Identify the common factors.
Common factors: 1, 2, 3, 4, 6, 12
Step 3: Choose the highest common factor.
The highest common factor from the list is 12.
Step 4: Check if the GCF is correct.
Now, divide both original numbers by the GCF to check:
36 ÷ 12 = 3
48 ÷ 12 = 4
Since both divisions result in whole numbers with no remainders, the GCF of 36 and 48 is indeed 12, which we had determined using the boomerang method.