Kyle works out that the HCF of the two numbers is:
2squared x 3squared=36
What two numbers might Kyle have been using?
To find the two numbers that Kyle might have been using, we need to calculate the factors of 36.
The factors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18, 36
Since Kyle mentioned that the highest common factor (HCF) is 2 squared (which is 4) multiplied by 3 squared (which is 9), we can look for numbers whose factors include these two numbers.
One possible pair of numbers that Kyle might have been using is 36 and 4 because 4 and 9 are factors of both numbers.
Therefore, Kyle might have been using the numbers 36 and 4.
To determine the two numbers that Kyle might have been using, we can find the prime factorization of the HCF (Highest Common Factor) which is given as 36.
Step 1: Prime Factorization of 36
To find the prime factorization of 36, we divide it by its smallest prime factor, which is 2.
36 ÷ 2 = 18
Then, we divide the quotient (18) by its smallest prime factor, which is again 2.
18 ÷ 2 = 9
Next, we divide 9 by its smallest prime factor, which is 3.
9 ÷ 3 = 3
Now, we are left with 3, which is already a prime number.
So, the prime factorization of 36 is 2 × 2 × 3 × 3, which is written as 2^2 × 3^2.
Step 2: Determining the Two Numbers
From the prime factorization, we can determine the numbers Kyle might have been using:
One number would be 2^2 (2 squared), which is equal to 4.
The other number would be 3^2 (3 squared), which is equal to 9.
Therefore, Kyle might have been using the numbers 4 and 9.