QuestionIs the number 15 prime, composite, or neither?

Studdy Solution

STEP 1

Assumptions1. The number we are examining is15.

STEP 2

A prime number is a natural number greater than1 that has no positive divisors other than1 and itself. The first few prime numbers are2,,5,7,11, and13.

STEP 3

A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, a composite number is any positive integer greater than one that is not a prime number.

STEP 4

To determine if15 is prime, composite, or neither, we need to find its divisors. A divisor is a number that divides another number evenly, i.e., without leaving a remainder.

STEP 5

We start by checking if15 can be divided evenly by2. $15 \, mod \,2$

STEP 6

Calculate the modulus.
$15 \, mod \,2 =1$

STEP 7

Since the result is not zero,2 is not a divisor of15. We move on to the next number,3.
$15 \, mod \,3$

STEP 8

Calculate the modulus.
$15 \, mod \,3 =0$

STEP 9

Since the result is zero,3 is a divisor of15. This means that15 is not a prime number, as it has more divisors than just and itself.

STEP 10

We continue checking for more divisors to confirm if15 is a composite number. We check the next number,4.
$15 \, mod \,4$

STEP 11

Calculate the modulus.
$15 \, mod \,4 =3$

STEP 12

Since the result is not zero,4 is not a divisor of15. We move on to the next number,5.
$15 \, mod \,5$

STEP 13

Calculate the modulus.
$15 \, mod \,5 =0$

STEP 14

Since the result is zero, is a divisor of. This confirms that is a composite number, as it has more than two divisors (,3,, and).
The number is a composite number.

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QuestionIs the number 15 prime, composite, or neither?

Studdy Solution

STEP 1

Assumptions1. The number we are examining is15.

STEP 2

A prime number is a natural number greater than1 that has no positive divisors other than1 and itself. The first few prime numbers are2,,5,7,11, and13.

STEP 3

A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, a composite number is any positive integer greater than one that is not a prime number.

STEP 4

To determine if15 is prime, composite, or neither, we need to find its divisors. A divisor is a number that divides another number evenly, i.e., without leaving a remainder.

STEP 5

We start by checking if15 can be divided evenly by2. $15 \, mod \,2$

STEP 6

Calculate the modulus.
$15 \, mod \,2 =1$

STEP 7

Since the result is not zero,2 is not a divisor of15. We move on to the next number,3.
$15 \, mod \,3$

STEP 8

Calculate the modulus.
$15 \, mod \,3 =0$

STEP 9

Since the result is zero,3 is a divisor of15. This means that15 is not a prime number, as it has more divisors than just and itself.

STEP 10

We continue checking for more divisors to confirm if15 is a composite number. We check the next number,4.
$15 \, mod \,4$

STEP 11

Calculate the modulus.
$15 \, mod \,4 =3$

STEP 12

Since the result is not zero,4 is not a divisor of15. We move on to the next number,5.
$15 \, mod \,5$

STEP 13

Calculate the modulus.
$15 \, mod \,5 =0$

STEP 14

Since the result is zero, is a divisor of. This confirms that is a composite number, as it has more than two divisors (,3,, and).
The number is a composite number.

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QuestionIs the number 15 prime, composite, or neither?

Studdy Solution

STEP 1

Assumptions1. The number we are examining is15.

STEP 2

A prime number is a natural number greater than1 that has no positive divisors other than1 and itself. The first few prime numbers are2,,5,7,11, and13.

STEP 3

A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, a composite number is any positive integer greater than one that is not a prime number.

STEP 4

To determine if15 is prime, composite, or neither, we need to find its divisors. A divisor is a number that divides another number evenly, i.e., without leaving a remainder.

STEP 5

We start by checking if15 can be divided evenly by2.15 mod 215 \, mod \,215mod2

STEP 6

Calculate the modulus.15 mod 2=115 \, mod \,2 =115mod2=1

STEP 7

Since the result is not zero,2 is not a divisor of15. We move on to the next number,3.15 mod 315 \, mod \,315mod3

STEP 8

Calculate the modulus.15 mod 3=015 \, mod \,3 =015mod3=0

STEP 9

Since the result is zero,3 is a divisor of15. This means that15 is not a prime number, as it has more divisors than just and itself.

STEP 10

We continue checking for more divisors to confirm if15 is a composite number. We check the next number,4.15 mod 415 \, mod \,415mod4

STEP 11

Calculate the modulus.15 mod 4=315 \, mod \,4 =315mod4=3

STEP 12

Since the result is not zero,4 is not a divisor of15. We move on to the next number,5.15 mod 515 \, mod \,515mod5

STEP 13

Calculate the modulus.15 mod 5=015 \, mod \,5 =015mod5=0

STEP 14

Since the result is zero, is a divisor of. This confirms that is a composite number, as it has more than two divisors (,3,, and).The number is a composite number.

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We start by checking if15 can be divided evenly by2. $15 \, mod \,2$

Calculate the modulus.
$15 \, mod \,2 =1$

Since the result is not zero,2 is not a divisor of15. We move on to the next number,3.
$15 \, mod \,3$

Calculate the modulus.
$15 \, mod \,3 =0$

We continue checking for more divisors to confirm if15 is a composite number. We check the next number,4.
$15 \, mod \,4$

Calculate the modulus.
$15 \, mod \,4 =3$

Since the result is not zero,4 is not a divisor of15. We move on to the next number,5.
$15 \, mod \,5$

Calculate the modulus.
$15 \, mod \,5 =0$

Since the result is zero, is a divisor of. This confirms that is a composite number, as it has more than two divisors (,3,, and).
The number is a composite number.