To determine the highest common factor (HCF) of the given numbers, you need to find the largest number that divides all the given numbers evenly.
a) For the numbers 12, 48, and 60:
- List the factors of each number:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- The common factors are 1, 2, 3, and 6. Therefore, the HCF of 12, 48, and 60 is 6.
b) For the numbers 6x and 8xy:
- Find the factors of each expression:
- Factors of 6x: 1, 2, 3, 6, x, 2x, 3x, 6x
- Factors of 8xy: 1, 2, 4, 8, x, y, 2x, 4x, 8x, 2y, 4y, 8y, 2xy, 4xy, 8xy
- The only common factor is 2. Thus, the HCF of 6x and 8xy is 2.
c) For the number 63:
- List the factors of 63: 1, 3, 7, 9, 21, 63
- Since 63 is a prime number, its only factor is 1. Hence, the HCF of 63 is 1.
d) For the number 4:
- List the factors of 4: 1, 2, 4
- The only common factor is 1. Therefore, the HCF of 4 is 1.
In summary:
a) HCF of 12, 48, and 60 is 6
b) HCF of 6x and 8xy is 2
c) HCF of 63 is 1
d) HCF of 4 is 1
This process helps to identify the highest common factor of the given numbers or expressions by finding their common factors and determining the largest one.
