how can the whole number 125 be expressed as a product of prime numbers with exponents
To express the whole number 125 as a product of prime numbers with exponents, we first need to find the prime factorization of 125. Here's how to do it:
Step 1: Start by dividing 125 by the smallest prime number, which is 2. Since 125 is not divisible evenly by 2, move on to the next prime number.
Step 2: Divide 125 by the next prime number, which is 3. Again, 125 is not divisible evenly by 3.
Step 3: Divide 125 by the next prime number, which is 5. This time, 125 is divisible evenly by 5. So, 125 divided by 5 is 25.
Step 4: Repeat the process with the quotient (25) from the previous step. Divide 25 by the smallest prime number, which is 2. Again, 25 is not divisible evenly by 2.
Step 5: Divide 25 by the next prime number, which is 3. Once again, 25 is not divisible evenly by 3.
Step 6: Divide 25 by the next prime number, which is 5. This time, 25 divided by 5 is 5.
Now, we have reached a prime number. 5 cannot be divided further since it is a prime number.
Hence, the prime factorization of 125 is 5 * 5 * 5, or in exponent form: 5^3.
fine the gcf of 15q + 6
To find the greatest common factor (GCF) of 15q + 6, we need to identify the common factors between the two terms. We can do this by factoring out the common factors.
First, let's look at the terms 15q and 6. The common factor between them is 3. We can factor out 3 from each term:
15q can be expressed as 3 * 5q.
6 can be expressed as 3 * 2.
Now, we have 3 * 5q + 3 * 2. We can factor out the 3 once again:
3 * (5q + 2).
Hence, the GCF of 15q + 6 is 3.
find the gcf of 8d - 20
Factor 9z + 18 using the GCF.(1 point)
To factor 9z + 18 using the greatest common factor (GCF), we need to identify the common factors between the two terms and factor them out.
The GCF of 9z and 18 is 9, since both terms are divisible by 9. We can factor out 9 from both terms:
9z can be expressed as 9 * z.
18 can be expressed as 9 * 2.
Now, we have 9 * z + 9 * 2. We can factor out the 9:
9 * (z + 2).
Hence, the factored form of 9z + 18 using the GCF is 9(z + 2).
Factor 16d − 12 using the GCF.(1 point)
To factor 16d - 12 using the greatest common factor (GCF), we need to identify the common factors between the two terms and factor them out.
First, let's find the GCF of 16d and 12. Both terms are divisible by 4, so the GCF is 4.
Now, let's factor out 4 from both terms:
16d can be expressed as 4 * 4d.
12 can be expressed as 4 * 3.
Now, we have 4 * 4d - 4 * 3. We can factor out the 4:
4 * (4d - 3).
Therefore, the factored form of 16d - 12 using the GCF is 4(4d -3).