prime factorization of 87750 in exponent form
how do I start with this
this looks like a good explanation studyzone . org/mtestprep/math8/a/primefactors7l . cfm
start with small factors
87750 = 2x5x5x5x3x3x3x13
or you could break it up into bigger chunks, which you then reduce
87750 = 50 x 5x3x3x3x13
= 5x5x2x5x3x3x3x13
= 2x3x3x3x5x5x5x13
To begin prime factorization of a number, you need to divide it by prime numbers starting from the smallest prime number, which is 2, and continue dividing until you can no longer divide any further. Let's go step by step to find the prime factorization of 87750.
Step 1: Divide by 2
Divide 87750 by 2:
87750 ÷ 2 = 43875.
Step 2: Divide by 3
Now, divide the quotient (43875) obtained from the previous step by the next prime number, which is 3:
43875 ÷ 3 = 14625.
Step 3: Divide by 3 again
Continue dividing by 3 until you can no longer divide evenly:
14625 ÷ 3 = 4875.
Step 4: Divide by 5
Next, divide the quotient (4875) by 5:
4875 ÷ 5 = 975.
Step 5: Divide by 5 again
Continue dividing by 5 until no further division is possible:
975 ÷ 5 = 195.
Step 6: Divide by 13
Now divide the quotient (195) by the prime number 13:
195 ÷ 13 = 15.
Step 7: Divide by 3
Finally, divide the quotient (15) by the prime number 3:
15 ÷ 3 = 5.
Now, we have divided 87750 until we reached 5, which is also a prime number. To express the prime factorization in exponent form, we combine the factors:
87750 = 2^1 × 3^3 × 5^3 × 13^1
So, the prime factorization of 87750 in exponent form is 2^1 × 3^3 × 5^3 × 13^1.