Question

A number that has no factors in common with another number (3 & 7).

A) Prime Numbers
B) Composite Numbers
C) Co-Prime Numbers
D) Rational Numbers

Answer 1

Step-by-step explanation:

The correct answer is:

C) Co-Prime Numbers

Co-prime numbers, also known as relatively prime or mutually prime numbers, are numbers that have no common factors other than 1. In other words, when two numbers are co-prime, their greatest common divisor (GCD) is equal to 1.

In the given example, the numbers 3 and 7 are co-prime because they do not have any factors in common other than 1. The factors of 3 are 1 and 3, while the factors of 7 are 1 and 7. Since they do not share any common factors other than 1, they are considered co-prime.

Here is a breakdown of the other answer choices:

A) Prime Numbers: Prime numbers are positive integers greater than 1 that have only two distinct positive divisors: 1 and the number itself. For example, 3 and 7 are prime numbers because they only have two factors.

B) Composite Numbers: Composite numbers are positive integers greater than 1 that have more than two factors. They can be factored into smaller positive integers other than 1 and the number itself. For example, 6 is a composite number because it can be factored into 2 and 3.

D) Rational Numbers: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. They include both integers and fractions. While 3 and 7 are rational numbers, the term "rational numbers" does not specifically refer to numbers with no common factors.

Therefore, the correct answer is C) Co-Prime Numbers, as it accurately describes numbers that have no factors in common with each other, such as 3 and 7 in the given example.

Answer 2

The answer to the student's question is 'Co-Prime Numbers'. Co-Prime Numbers are numbers that have no factors in common except for 1. They may be prime or composite, but the lack of shared factors, other than 1, is what defines them as co-prime.

Step-by-step explanation:

A number that has no factors in common with another number (like the numbers 3 and 7) are referred to as Co-Prime Numbers. Prime numbers are numbers that have only two distinct positive divisors: 1 and the number itself. Composite numbers are numbers that have more than two factors. Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Co-prime numbers may or may not be prime, but the defining characteristic is that they share no common factors other than 1.

The concept of mutual exclusivity in probability states that two events cannot both occur at the same time. Using this concept in the context of numbers, if A and C have no numbers in common, the probability of them both occurring is 0, indicating they are mutually exclusive - this relates to the concept of co-prime numbers. When the mutual exclusivity of two sets, such as A and B, is not known, it is assumed that they are not mutually exclusive until proven otherwise.

As for numbers, they are composed of digits which are the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The digits are combined to form numbers, and when the decimal point is not explicitly written, it is usually implied to be at the end of the whole number, shown by convention in a red font.