Fun Math Quiz on Highest Common Factor

HCF stands for Highest Common Factor, which refers to the largest integer that divides two or more numbers without leaving a remainder. It is a fundamental concept in number theory used to simplify fractions, find common denominators, and solve problems involving divisibility. Understanding HCF helps in various mathematical applications, including algebra and geometry, as it allows for the identification of relationships between numbers and their factors.

A factor of a number is an integer that divides that number without leaving a remainder. In this case, 12 can be divided by 3, resulting in 4 (12 ÷ 3 = 4), which confirms that 3 is indeed a factor of 12. The other options, 5, 7, and 9, do not divide 12 evenly, as they leave a remainder. Therefore, 3 is the only correct choice among the options provided.

To find the highest common factor (HCF) of 8 and 12, we identify the factors of each number. The factors of 8 are 1, 2, 4, and 8, while the factors of 12 are 1, 2, 3, 4, 6, and 12. The common factors between them are 1, 2, and 4. Among these, the largest is 4, making it the highest common factor. This means 4 is the greatest number that can evenly divide both 8 and 12.

Two numbers have an HCF (Highest Common Factor) of 1 when they are coprime, meaning they share no common factors other than 1. In this case, 2 and 3 are both prime numbers, and their only common factor is indeed 1. In contrast, the other pairs share common factors greater than 1: 4 and 6 share 2, 8 and 12 share 4, and 10 and 15 share 5. Therefore, the pair 2 and 3 stands out as having an HCF of 1.

To find the highest common factor (HCF) of 14 and 21, we identify the factors of each number. The factors of 14 are 1, 2, 7, and 14, while the factors of 21 are 1, 3, 7, and 21. The common factors are 1 and 7, with 7 being the largest. Therefore, the HCF of 14 and 21 is 7, as it is the greatest number that divides both without leaving a remainder.

A common factor is a number that divides two or more numbers without leaving a remainder. For 6 and 9, the factors are as follows: 6 has factors 1, 2, 3, and 6; while 9 has factors 1, 3, and 9. The only number that appears in both lists is 3. Therefore, 3 is a common factor of 6 and 9, as it divides both numbers evenly.

To find the largest common factor of 12 and 18, we first identify the factors of each number. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors between the two sets are 1, 2, 3, and 6. Among these, the largest is 6, making it the greatest common factor of 12 and 18.

When two numbers are prime, they have no common factors other than 1. Prime numbers are defined as having exactly two distinct positive divisors: 1 and themselves. Since they do not share any other divisors, the highest common factor (HCF) of two prime numbers is always 1. This means that regardless of the size of the prime numbers, their only shared factor is 1.

To find the highest common factor (HCF) of 20 and 30, we identify the factors of each number. The factors of 20 are 1, 2, 4, 5, 10, and 20, while the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The common factors are 1, 2, 5, and 10. Among these, the highest is 10, making it the HCF of 20 and 30. This means 10 is the largest number that divides both 20 and 30 without leaving a remainder.

To determine which number is not a factor of 18, we need to identify the numbers that divide 18 without leaving a remainder. The factors of 18 are 1, 2, 3, 6, 9, and 18. Among the options provided, 1, 2, and 9 are factors of 18, while 5 is not, as 18 cannot be evenly divided by 5. Therefore, 5 is the only number listed that does not qualify as a factor of 18.