Burns Martin
08/27/2024 · Junior High School
Which of the following statements are TRUE? Select ALL that ap 12 is a factor of 6 . The number 119 is a composite number. If a number is divisible by 3 and by 4 , then it is divisible by 12 . If a number is divisible by 6 and by 4 , then it is divisible by 24 . All even numbers are composite numbers. All prime numbers are odd numbers.
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Step-by-step Solution
To determine which of the following statements are TRUE, let's analyze each statement:
1. 12 is a factor of 6:
- This statement is TRUE. 12 is a factor of 6 because 6 divided by 12 equals 0.5.
2. The number 119 is a composite number:
- This statement is FALSE. 119 is a prime number because it is only divisible by 1 and itself.
3. If a number is divisible by 3 and by 4, then it is divisible by 12:
- This statement is TRUE. If a number is divisible by both 3 and 4, it is divisible by their least common multiple, which is 12.
4. If a number is divisible by 6 and by 4, then it is divisible by 24:
- This statement is TRUE. If a number is divisible by both 6 and 4, it is divisible by their least common multiple, which is 24.
5. All even numbers are composite numbers:
- This statement is FALSE. Even numbers can be prime numbers as well. For example, 2 is an even prime number.
6. All prime numbers are odd numbers:
- This statement is FALSE. 2 is a prime number and an even number, so not all prime numbers are odd.
Therefore, the TRUE statements are:
- 12 is a factor of 6.
- If a number is divisible by 3 and by 4, then it is divisible by 12.
- If a number is divisible by 6 and by 4, then it is divisible by 24.
Quick Answer
- 12 is a factor of 6.
- If a number is divisible by 3 and by 4, then it is divisible by 12.
- If a number is divisible by 6 and by 4, then it is divisible by 24.
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