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Determine the number that 88 is divisible by from the choices provided.(1 point)
Responses

3
3

2
2

5
5

6

9 answers

To determine which numbers 88 is divisible by, we can check each option:

  1. 3: A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits in 88 is 8 + 8 = 16, which is not divisible by 3. So, 88 is not divisible by 3.

  2. 2: A number is divisible by 2 if it is even. Since 88 is even, it is divisible by 2.

  3. 5: A number is divisible by 5 if it ends in 0 or 5. Since 88 ends in 8, it is not divisible by 5.

  4. 6: A number is divisible by 6 if it is divisible by both 2 and 3. We already established that 88 is divisible by 2 but not by 3, so it is not divisible by 6.

From the options provided, the only number that 88 is divisible by is 2.

Determine the number greater than 19 and less than 34 that is divisible by 6 and 10.(1 point)
Responses

24
24

30
30

60
60

20

To find a number greater than 19 and less than 34 that is divisible by both 6 and 10, we first need to determine the least common multiple (LCM) of 6 and 10.

The LCM of 6 and 10 can be found by:

  • The prime factors of 6 are: \(2 \times 3\)
  • The prime factors of 10 are: \(2 \times 5\)

To find the LCM, take the highest power of each prime that appears in the factorization:

  • From 6: \(2^1, 3^1\)
  • From 10: \(2^1, 5^1\)

So, the LCM is: \[ 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30 \]

Now, we check if 30 falls within the specified range:

  • Is 30 greater than 19? Yes.
  • Is 30 less than 34? Yes.

Thus, the only number greater than 19 and less than 34 that is divisible by both 6 and 10 is:

30.

Identify the number classified as prime.(1 point)
Responses

29
29

39
39

49
49

69
69

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Let's check each of the provided numbers:

  1. 29: The only divisors are 1 and 29. So, 29 is a prime number.

  2. 39: The divisors are 1, 3, 13, and 39. So, 39 is not a prime number.

  3. 49: The divisors are 1, 7, and 49. So, 49 is not a prime number since it can be divided by 7.

  4. 69: The divisors are 1, 3, 23, and 69. So, 69 is not a prime number.

Therefore, the number classified as prime from the given options is:

29.

Identify the number classified as composite.(1 point)
Responses

27
27

37
37

67
67

47

A composite number is a natural number greater than 1 that is not prime, meaning it has positive divisors other than 1 and itself. Let's evaluate each of the provided numbers:

  1. 27: The divisors are 1, 3, 9, and 27. Since it has divisors other than 1 and itself, 27 is a composite number.

  2. 37: The only divisors are 1 and 37. So, 37 is a prime number, not composite.

  3. 67: The only divisors are 1 and 67. So, 67 is also a prime number, not composite.

  4. 47: The only divisors are 1 and 47. So, 47 is also a prime number, not composite.

From the choices given, the number classified as composite is:

27.

Classify zero (0) as prime or composite.(1 point)
Responses

composite
composite

both prime and composite
both prime and composite

prime
prime

neither prime nor composite

Zero (0) is neither classified as a prime nor a composite number. Here’s why:

  • Prime Number: A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. Since 0 is not greater than 1, it cannot be classified as prime.

  • Composite Number: A composite number is defined as a natural number greater than 1 that has more than two distinct positive divisors. Again, since 0 is not greater than 1, it cannot be classified as composite either.

Thus, the correct classification for zero is:

neither prime nor composite.