What is the highest common factor of 40 and 72?
Understand the Problem
The question is asking for the highest common factor (HCF) of the numbers 40 and 72. This involves identifying the largest number that divides both numbers without leaving a remainder.
Answer
The HCF of 40 and 72 is $8$.
Answer for screen readers
The highest common factor of 40 and 72 is $8$.
Steps to Solve
- Find the Prime Factorization of 40
To find the HCF, start by determining the prime factors of 40.
The prime factorization of 40 is:
$$ 40 = 2^3 \times 5^1 $$
- Find the Prime Factorization of 72
Next, find the prime factors of 72.
The prime factorization of 72 is:
$$ 72 = 2^3 \times 3^2 $$
- Identify Common Prime Factors
Look for the prime factors that both numbers have in common and note their lowest powers.
The common prime factor is 2, and the lowest power is $2^3$.
- Calculate the HCF
Multiply the common prime factors together:
$$ HCF = 2^3 = 8 $$
The highest common factor of 40 and 72 is $8$.
More Information
The highest common factor (HCF) represents the largest integer that divides both numbers without any remainders. Understanding how to factor numbers can greatly help with finding the HCF.
Tips
- Not correctly identifying the prime factors of each number. To avoid this, carefully divide the number by the smallest prime until you cannot divide anymore.
- Forgetting to take the lowest power of common prime factors. It’s important to compare the exponents of common factors to determine the HCF correctly.
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