Number Theory And Fractions

The GCF (Greatest Common Factor) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the numbers 5 and 7 do not have any common factors other than 1, so the GCF is 1. Therefore, none of the given options (25, 45, 35) is the correct answer.

760 is a multiple of 5 because it is divisible by 5 without leaving any remainder. When 760 is divided by 5, the result is 152, which means that 760 can be evenly divided into 5 equal parts. Therefore, the statement "760 is a multiple of 5" is true.

An improper fraction is a fraction where the numerator is equal to or greater than the denominator. In the given fraction 7/8, the numerator (7) is less than the denominator (8), making it a proper fraction. Therefore, the correct answer is False.

The LCM (Least Common Multiple) is the smallest multiple that is divisible by both numbers. In this case, the multiples of 9 are 9, 18, 27, 36, ... and the multiples of 6 are 6, 12, 18, 24, .... The smallest multiple that is common to both 9 and 6 is 18, so it is the LCM of 9 and 6.

A prime number is a number that is only divisible by 1 and itself. In the case of 17, it cannot be divided evenly by any other number except 1 and 17. Therefore, 17 is a prime number.

A common multiple of two numbers is a number that can be divided evenly by both numbers. In this case, the common multiples of 6 and 18 are numbers that can be divided evenly by both 6 and 18. Out of the given options, only 36 can be divided evenly by both 6 and 18. Therefore, 36 is the correct answer.

A proper fraction is a fraction where the numerator is smaller than the denominator. In the given fraction 5/8, the numerator (5) is smaller than the denominator (8), making it a proper fraction.

The LCM (Least Common Multiple) of two numbers is the smallest multiple that is divisible by both numbers. In this case, the LCM of 4 and 15 is 60, not 40. Therefore, the given statement is false.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In this case, the fraction 24/14 is an improper fraction because the numerator (24) is greater than the denominator (14).

The prime factorization of a number involves finding the prime numbers that multiply together to give the original number. In this case, the prime factorization of 95 is 5 x 19. Therefore, the missing number that completes the prime factorization is 19.

The fraction 24/32 is equivalent to 6/8 because both fractions can be simplified to 3/4. To simplify 24/32, we divide both the numerator and denominator by their greatest common divisor, which is 8. This gives us 3/4. Therefore, 24/32 is equivalent to 6/8.

To find 3/8 of 24, we multiply 24 by 3/8. Multiplying 24 by 3 gives us 72, and dividing 72 by 8 gives us 9. Therefore, 3/8 of 24 is 9.

The number 8 is the least number that has both 2 and 4 as factors. This is because 8 can be divided evenly by both 2 and 4. In other words, 8 is divisible by 2 and 4 without leaving any remainder. The other options, 6, 10, and 3, do not have both 2 and 4 as factors, making 8 the correct answer.

The fraction 4/7 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4. This results in the simplified fraction 1/2. Therefore, the correct answer is 16/28, which is also equal to 1/2 when simplified.

To find 5/8 of 24, we can multiply 24 by 5/8. Multiplying 24 by 5 gives us 120, and dividing that by 8 gives us 15. Therefore, 15 is 5/8 of 24.

A prime number is a number that is only divisible by 1 and itself. In this case, 27 is not a prime number because it is divisible by 1, 3, 9, and 27. Therefore, the correct answer is False.

A prime number is a number greater than 1 that is divisible only by 1 and itself. Since 33 is divisible by 3 and 11 in addition to 1 and 33, it is not a prime number. Therefore, the correct answer is False.

The prime factorization of 80 is 5 x 2 x 2 x 2 x 2. This means that 80 can be expressed as the product of these prime numbers.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In the given fraction 18/16, the numerator (18) is greater than the denominator (16), making it an improper fraction.

A common multiple of two numbers is a number that is divisible by both of the given numbers. In this case, we need to find a number that is divisible by both 6 and 14. The numbers 28, 24, and 32 are not divisible by both 6 and 14. However, 42 is divisible by both 6 (6 x 7 = 42) and 14 (14 x 3 = 42), making it a common multiple of 6 and 14.

To find 2/6 of a number, you can divide that number by 6 and then multiply the result by 2. In this case, if we divide 36 by 6, we get 6. Multiplying 6 by 2 gives us 12, which is indeed 2/6 of 36. Therefore, the correct answer is 36.

The greatest common factor (GCF) is the largest number that divides evenly into both 12 and 20. In this case, the factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 20 are 1, 2, 4, 5, 10, and 20. The largest number that appears in both lists is 4, so that is the GCF of 12 and 20.

The greatest common factor (GCF) is the largest number that divides two numbers evenly. In this case, the numbers 6 and 7 do not have any common factors other than 1. Therefore, the GCF of 6 and 7 is 1.

The fraction 24/36 is equivalent to 2/3 because both fractions can be simplified to 2/3 by dividing the numerator and denominator by their greatest common divisor, which is 12. Similarly, the fraction 4/9 is also equivalent to 2/3 because both fractions can be simplified to 2/3 by dividing the numerator and denominator by their greatest common divisor, which is 2.