QuestionFind factor pairs of 27 and circle the prime numbers among them.

Studdy Solution

STEP 1

Assumptions1. We are looking for pairs of numbers that when multiplied together give27. We are also looking to identify which of these numbers are prime. A prime number is a number that has exactly two distinct positive divisors1 and itself.

STEP 2

We start by finding the pairs of factors. A good way to do this is to start from1 and try to divide27 by increasing numbers. If the division results in an integer, then we have found a pair of factors.

STEP 3

First, we try1. $27 /1 =27$ This means1 and27 are a pair of factors.

STEP 4

Next, we try2. $27 /2 =13.$ This is not an integer, so2 is not a factor of27.

STEP 5

We continue this process with3.
$27 /3 =9$ So,3 and9 are a pair of factors.

STEP 6

We continue with4.
$27 /4 =6.75$ This is not an integer, so4 is not a factor of27.

STEP 7

We continue with5.
$27 /5 =5.4$ This is not an integer, so5 is not a factor of27.

STEP 8

We continue with6.
$27 /6 =4.5$ This is not an integer, so6 is not a factor of27.

STEP 9

We continue with7.
$27 /7 \approx3.857$ This is not an integer, so7 is not a factor of27.

STEP 10

We continue with8.
$27 /8 =3.375$ This is not an integer, so8 is not a factor of27.

STEP 11

We continue with9.
$27 /9 =3$ So,9 and3 are a pair of factors. However, this pair is the same as the pair3 and9 that we found earlier, so we can stop here.

STEP 12

Now we have all the factor pairs of27 (,27) and (,9).

STEP 13

Next, we need to identify the prime numbers among these factors.

STEP 14

is not a prime number by definition, even though it has only one positive divisor, because a prime number must have exactly two distinct positive divisors.

STEP 15

27 is not a prime number, because it has more than two distinct positive divisors (,3,9, and27).

STEP 16

3 is a prime number, because it has exactly two distinct positive divisors ( and3).

STEP 17

9 is not a prime number, because it has three distinct positive divisors (,3, and9).
So, the only prime number among the factors of27 is3.

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QuestionFind factor pairs of 27 and circle the prime numbers among them.

Studdy Solution

STEP 1

Assumptions1. We are looking for pairs of numbers that when multiplied together give27. We are also looking to identify which of these numbers are prime. A prime number is a number that has exactly two distinct positive divisors1 and itself.

STEP 2

We start by finding the pairs of factors. A good way to do this is to start from1 and try to divide27 by increasing numbers. If the division results in an integer, then we have found a pair of factors.

STEP 3

First, we try1. $27 /1 =27$ This means1 and27 are a pair of factors.

STEP 4

Next, we try2. $27 /2 =13.$ This is not an integer, so2 is not a factor of27.

STEP 5

We continue this process with3.
$27 /3 =9$ So,3 and9 are a pair of factors.

STEP 6

We continue with4.
$27 /4 =6.75$ This is not an integer, so4 is not a factor of27.

STEP 7

We continue with5.
$27 /5 =5.4$ This is not an integer, so5 is not a factor of27.

STEP 8

We continue with6.
$27 /6 =4.5$ This is not an integer, so6 is not a factor of27.

STEP 9

We continue with7.
$27 /7 \approx3.857$ This is not an integer, so7 is not a factor of27.

STEP 10

We continue with8.
$27 /8 =3.375$ This is not an integer, so8 is not a factor of27.

STEP 11

We continue with9.
$27 /9 =3$ So,9 and3 are a pair of factors. However, this pair is the same as the pair3 and9 that we found earlier, so we can stop here.

STEP 12

Now we have all the factor pairs of27 (,27) and (,9).

STEP 13

Next, we need to identify the prime numbers among these factors.

STEP 14

is not a prime number by definition, even though it has only one positive divisor, because a prime number must have exactly two distinct positive divisors.

STEP 15

27 is not a prime number, because it has more than two distinct positive divisors (,3,9, and27).

STEP 16

3 is a prime number, because it has exactly two distinct positive divisors ( and3).

STEP 17

9 is not a prime number, because it has three distinct positive divisors (,3, and9).
So, the only prime number among the factors of27 is3.

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QuestionFind factor pairs of 27 and circle the prime numbers among them.

Studdy Solution

STEP 1

Assumptions1. We are looking for pairs of numbers that when multiplied together give27. We are also looking to identify which of these numbers are prime. A prime number is a number that has exactly two distinct positive divisors1 and itself.

STEP 2

We start by finding the pairs of factors. A good way to do this is to start from1 and try to divide27 by increasing numbers. If the division results in an integer, then we have found a pair of factors.

STEP 3

First, we try1.27/1=2727 /1 =2727/1=27This means1 and27 are a pair of factors.

STEP 4

Next, we try2.27/2=13.27 /2 =13.27/2=13.This is not an integer, so2 is not a factor of27.

STEP 5

We continue this process with3.27/3=927 /3 =927/3=9So,3 and9 are a pair of factors.

STEP 6

We continue with4.27/4=6.7527 /4 =6.7527/4=6.75This is not an integer, so4 is not a factor of27.

STEP 7

We continue with5.27/5=5.427 /5 =5.427/5=5.4This is not an integer, so5 is not a factor of27.

STEP 8

We continue with6.27/6=4.527 /6 =4.527/6=4.5This is not an integer, so6 is not a factor of27.

STEP 9

We continue with7.27/7≈3.85727 /7 \approx3.85727/7≈3.857This is not an integer, so7 is not a factor of27.

STEP 10

We continue with8.27/8=3.37527 /8 =3.37527/8=3.375This is not an integer, so8 is not a factor of27.

STEP 11

We continue with9.27/9=327 /9 =327/9=3So,9 and3 are a pair of factors. However, this pair is the same as the pair3 and9 that we found earlier, so we can stop here.

STEP 12

Now we have all the factor pairs of27 (,27) and (,9).

STEP 13

Next, we need to identify the prime numbers among these factors.

STEP 14

is not a prime number by definition, even though it has only one positive divisor, because a prime number must have exactly two distinct positive divisors.

STEP 15

27 is not a prime number, because it has more than two distinct positive divisors (,3,9, and27).

STEP 16

3 is a prime number, because it has exactly two distinct positive divisors ( and3).

STEP 17

9 is not a prime number, because it has three distinct positive divisors (,3, and9).So, the only prime number among the factors of27 is3.

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First, we try1. $27 /1 =27$ This means1 and27 are a pair of factors.

Next, we try2. $27 /2 =13.$ This is not an integer, so2 is not a factor of27.

We continue this process with3.
$27 /3 =9$ So,3 and9 are a pair of factors.

We continue with4.
$27 /4 =6.75$ This is not an integer, so4 is not a factor of27.

We continue with5.
$27 /5 =5.4$ This is not an integer, so5 is not a factor of27.

We continue with6.
$27 /6 =4.5$ This is not an integer, so6 is not a factor of27.

We continue with7.
$27 /7 \approx3.857$ This is not an integer, so7 is not a factor of27.

We continue with8.
$27 /8 =3.375$ This is not an integer, so8 is not a factor of27.

We continue with9.
$27 /9 =3$ So,9 and3 are a pair of factors. However, this pair is the same as the pair3 and9 that we found earlier, so we can stop here.

9 is not a prime number, because it has three distinct positive divisors (,3, and9).
So, the only prime number among the factors of27 is3.