Mastering Highest Common Factor for Grade 3

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 are 1, 2, and 4. Among these, the highest is 4, making it the HCF. This means that 4 is the largest number that can divide both 8 and 12 without leaving a remainder.

To find the highest common factor (HCF) of 10 and 15, we identify the factors of each number. The factors of 10 are 1, 2, 5, and 10, while the factors of 15 are 1, 3, 5, and 15. The common factors between the two sets are 1 and 5. Among these, the highest is 5, making it the HCF. This means 5 is the largest number that can evenly divide both 10 and 15.

To determine a common factor of 6 and 9, we identify the factors of each number. The factors of 6 are 1, 2, 3, and 6, while the factors of 9 are 1, 3, and 9. The factors they share are 1 and 3. Among these, 3 is the largest common factor, making it the most significant shared factor between the two numbers. Thus, 3 is the correct answer as it divides both 6 and 9 without leaving a remainder.

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.

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 between the two sets are 1 and 7. Among these, the highest is 7, making it the HCF. This means 7 is the largest number that divides both 14 and 21 without leaving a remainder.

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 the only divisor they share is 1, their highest common factor (HCF) is 1. This holds true regardless of the size of the prime numbers involved; thus, the HCF will always be 1 when considering any two prime numbers.

Factors of a number are integers that can be multiplied together to produce that number. For 12, the factors are 1, 2, 3, 4, 6, and 12. The number 5 cannot be multiplied by any integer to result in 12, making it not a factor of 12. Therefore, among the options provided, 5 is the only number that does not divide evenly into 12.

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.

To find the highest common factor (HCF) of 24 and 36, we can list the factors of each number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, while the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The common factors are 1, 2, 3, 4, 6, and 12. Among these, the highest is 12, making it the HCF of 24 and 36.

To determine a common factor of 15 and 25, we identify the factors of each number. The factors of 15 are 1, 3, 5, and 15, while the factors of 25 are 1, 5, and 25. The number 5 appears in both lists, making it a common factor. Since it is the largest number that divides both 15 and 25 without leaving a remainder, it is the most significant common factor between them.