HCF of 240, 336, 432, and 528
Understand the Problem
The question is asking for the highest common factor (HCF) of the numbers 240, 336, 432, and 528. To solve this, we will find the prime factorization of each number and then identify the common factors.
Answer
The HCF is $48$.
Answer for screen readers
The highest common factor (HCF) of 240, 336, 432, and 528 is 48.
Steps to Solve
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Prime Factorization of Each Number We start by finding the prime factorization of each of the numbers:
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For $240$: $$ 240 = 2^4 \times 3^1 \times 5^1 $$
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For $336$: $$ 336 = 2^4 \times 3^1 \times 7^1 $$
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For $432$: $$ 432 = 2^4 \times 3^3 $$
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For $528$: $$ 528 = 2^4 \times 3^1 \times 11^1 $$
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Identifying Common Prime Factors Next, we look for the common prime factors in all factorizations:
- The common prime factor is $2$ and $3$.
- The minimum power of $2$ across all numbers is $2^4$.
- The minimum power of $3$ across the numbers is $3^1$.
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Calculating the HCF Now we can calculate the HCF by multiplying the common factors: $$ HCF = 2^4 \times 3^1 $$
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Simplifying the Expression We simplify to find the numerical value: $$ HCF = 16 \times 3 = 48 $$
The highest common factor (HCF) of 240, 336, 432, and 528 is 48.
More Information
The highest common factor is the largest number that divides all given numbers without leaving a remainder. Knowing how to find the HCF is useful in simplifying fractions and finding ratios.
Tips
- Ignoring higher powers: When finding the HCF, it’s important to take the lowest power of each common prime factor, not the highest.
- Forgetting to check all numbers: Make sure to check all given numbers for common factors, as skipping one can lead to errors in the final answer.
