Use the divisibility rules to help determine the prime factorization of the number below. 87
A) $3 \cdot 28$
B) $3 \cdot 29$
C) $9.29$
D) $3.5 .29$
E) none of these

Question

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First we can use the divisibility rule for 3, which states that if the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3. In this case, 8 + 7 = 15, which is divisible by 3, so 87 is divisible by 3.

Next, we can use the divisibility rule for 9, which states that if the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9. We already know that 8 + 7 = 15, which is not divisible by 9, so we can rule out choices A and D, since they both involve a factor of 9.

Finally, we check whether 87 is divisible by any prime numbers between 3 and 29 (inclusive) that we haven't already ruled out. We can see that 87 is not divisible by 5 or any of the even numbers between 2 and 28, so the only prime factor left to check is 29. It turns out that 87 is divisible by 29 (you can check this by long division or a calculator), so the prime factorization of 87 is 3 * 29.

Use the Divisibility Rules to Help Determine the Prime Factorization 3⋅283 \cdot 283⋅28

Use the Divisibility Rules to Help Determine the Prime Factorization $3 \cdot 28$