What is the prime factorization of 1,050
Let's start by factoring out the obvious 50.
1050 = 50 * 21
The prime favors of 50 are 5*5*2
The prime factors of 21 are 3*7
The prime factors of 1050 are therefore
2*3*5*5*7
You could have done this problem other ways, but you'd get the same answer.
1050/2=525
525/5=105
105/5=21
21/7=3
all primes are 2,3,5,5,7
Have you ever tried factor trees?
1050
50 21
5 10 7 3
5 2
Factors: 5 5 2 7 3
These are fairly quick. Good luck!
do now and don't care
To find the prime factorization of 1,050, we need to find the prime numbers that divide it evenly. We start by dividing it by the smallest prime number, which is 2.
1,050 ÷ 2 = 525
Now we check if 525 is divisible by 2. It is not, so we move on to the next prime number, which is 3.
525 ÷ 3 = 175
Next, we check if 175 is divisible by 3. It is, so we continue dividing:
175 ÷ 3 = 58.33
58.33 is not a whole number, so 3 is not a factor of 175 anymore. We move on to the next prime number, which is 5.
175 ÷ 5 = 35
35 ÷ 5 = 7
Finally, 7 is a prime number, so we stop here because we cannot divide any further. Therefore, the prime factorization of 1,050 is:
2 × 3 × 5 × 5 × 7
or in exponential form:
2 × 3 × 5^2 × 7