What is the highest common factor of 28 and 70?
Understand the Problem
The question is asking for the highest common factor (HCF) of the numbers 28 and 70. To solve this, we would find all the factors of both numbers and identify the largest factor that they share.
Answer
The highest common factor (HCF) of 28 and 70 is $14$.
Answer for screen readers
The highest common factor (HCF) of 28 and 70 is $14$.
Steps to Solve
- Find the factors of 28
The factors of 28 are the numbers that divide 28 without leaving a remainder. Calculating, we find: $$ 28 = 1, 2, 4, 7, 14, 28 $$
- Find the factors of 70
Next, we find the factors of 70. Calculating, we have: $$ 70 = 1, 2, 5, 7, 10, 14, 35, 70 $$
- Identify the common factors
Now, we identify the factors that 28 and 70 have in common by comparing the two sets of factors: Common factors are: $$ 1, 2, 7, 14 $$
- Determine the highest common factor (HCF)
Finally, we choose the largest number from the common factors: The highest common factor (HCF) is: $$ HCF = 14 $$
The highest common factor (HCF) of 28 and 70 is $14$.
More Information
The highest common factor is useful in simplifying fractions or finding equivalent ratios. It helps determine the greatest amount that can be divided evenly among sets of numbers.
Tips
An example of a common mistake is forgetting to list all the factors or overlooking one of the common factors, which can lead to an incorrect HCF. Ensure to double-check the factors of both numbers thoroughly.
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