Write the prime factorization using exponents of each number .Then find the greatest common factor (GCF)of the numbers.
1\24..............
36..............
2\21..............
56..............
Please,,help me.😞
I tried to solve the problems but don't I know.
24 = 2^3 * 3
36 = 2^2 * 3^2
GCF = 2^2 * 3 = 12
21 = 3 * 7
56 = 2^3 * 7
GCF = 7
For the GCF, find the prime factors and their powers. Then multiply the smallest power of each prime that is common to both numbers.
Sure! Let's solve these step by step.
1) Prime factorization and GCF of 24 and 36:
To find the prime factorization of a number, we need to express it as a product of prime numbers.
Step 1: Prime factorization of 24
24 can be expressed as 2 * 2 * 2 * 3.
Step 2: Prime factorization of 36
36 can be expressed as 2 * 2 * 3 * 3.
Step 3: Find the GCF
To find the GCF, we need to determine the highest power of each common prime factor.
In this case, the common prime factors are 2 and 3. The highest power of 2 is 2 (since it appears three times in the prime factorization of 24 and only two times in the prime factorization of 36), and the highest power of 3 is also 2 (since it appears once in the prime factorization of 24 and twice in the prime factorization of 36).
Therefore, the GCF of 24 and 36 is 2 * 2 = 4.
2) Prime factorization and GCF of 21 and 56:
Step 1: Prime factorization of 21
21 can be expressed as 3 * 7.
Step 2: Prime factorization of 56
56 can be expressed as 2 * 2 * 2 * 7.
Step 3: Find the GCF
The common prime factor between 21 and 56 is 7. However, there are no other common prime factors between them.
Therefore, the GCF of 21 and 56 is 7.
So, the answers are:
1) Prime factorization of 24 is 2^3 * 3 and 36 is 2^2 * 3^2. The GCF of 24 and 36 is 4.
2) Prime factorization of 21 is 3 * 7 and 56 is 2^3 * 7. The GCF of 21 and 56 is 7.
Sure, I can help you with these problems.
To find the prime factorization of a number, you need to break it down into its prime factors. Prime factors are the prime numbers that multiply together to give the original number.
Let's solve the first problem:
1/24: To find the prime factorization of 24, we can start by dividing it by the smallest prime number, which is 2. 24 divided by 2 gives us 12. Now we divide 12 by 2 again, which gives us 6. Continuing this process, we divide 6 by 2 to get 3. Now, we cannot divide 3 by 2 anymore, so we move on to the next prime number, which is 3. Dividing 3 by 3 gives us 1.
Therefore, the prime factorization of 24 is 2^3 * 3^1.
Now let's find the prime factorization of 36:
36: We can start by dividing it by 2 since it is an even number. 36 divided by 2 gives us 18. Now we divide 18 by 2 again, which gives us 9. Again, we divide 9 by 3 to get 3. Finally, we divide 3 by 3 to get 1.
Therefore, the prime factorization of 36 is 2^2 * 3^2.
To find the greatest common factor (GCF) of these numbers, you need to determine the highest power of each prime factor that appears in both numbers.
For the GCF of 24 and 36, the prime factors are 2 and 3.
The power of 2 that appears in 24 is 3 (2^3) and in 36 is 2 (2^2). We take the lower power, which is 2.
The power of 3 that appears in 24 is 1 (3^1) and in 36 is 2 (3^2). Again, we take the lower power, which is 1.
Therefore, the GCF of 24 and 36 is 2^2 * 3^1, which is equal to 12.
Let's move on to the second problem now:
2/21: To find the prime factorization of 21, we can start by dividing it by 3. 21 divided by 3 gives us 7. Since 7 is a prime number, our prime factorization is complete.
Therefore, the prime factorization of 21 is 3^1 * 7^1.
Now let's find the prime factorization of 56:
56: We can start by dividing it by 2. 56 divided by 2 gives us 28. Now we divide 28 by 2 again to get 14. Continuing this process, we divide 14 by 2 to get 7. And 7 is a prime number, so our prime factorization is complete.
Therefore, the prime factorization of 56 is 2^3 * 7^1.
For the GCF of 21 and 56, the prime factors are 3 and 7.
The power of 3 that appears in 21 is 1 (3^1) and in 56 is 0 (3^0). We take the lower power, which is 0.
The power of 7 that appears in 21 is 1 (7^1) and in 56 is 1 (7^1). Both have the same power.
Therefore, the GCF of 21 and 56 is 3^0 * 7^1, which is equal to 7.
I hope this explanation helps you understand how to find the prime factorization and the GCF. Let me know if you have any further questions!