Write 1,386 as the product of its prime factors
A. 2 x 693
B. 2 x 3 x 231
C. 2 x 3 x 7 x 33
D. 2 x 3 x 3 x 7 x 11
what do you think
Each choice properly multiplies up to 1386, but D is the only choice that has all prime factors.
693, 231, and 33 aren't prime numbers since they can be factored further.
What do you think? Are 693, 231 and 33 prime numbers? Look at the list and think about it
To determine the prime factors of 1,386, we can follow a step-by-step process of repeatedly dividing the number by prime numbers until we can no longer divide evenly.
Begin by dividing 1,386 by the smallest prime number, 2:
1,386 ÷ 2 = 693
Since 693 is still divisible by 2, we divide it again:
693 ÷ 2 = 346.5
As 346.5 is not a whole number, we move on to the next prime number, 3:
693 ÷ 3 = 231
Since 231 is still divisible by 3, we divide it again:
231 ÷ 3 = 77
After dividing by 3, we find that 77 is not divisible by this prime number. We continue with the next prime number, 5, and so on. However, since none of the remaining prime numbers divide evenly into 77, we move to the next prime number, 7:
77 ÷ 7 = 11
We have reached a prime number. Since we cannot further divide 11, we stop here. Therefore, the prime factorization of 1,386 is:
1,386 = 2 × 3 × 3 × 7 × 11
Thus, the correct option is D. 2 x 3 x 3 x 7 x 11.