Math Problem Statement
Find the Highest Common Factor of x = 3 * 5^3 * 11^3 * 13^5 and y = 5 * 7 * 13^5. Give your answer in index form.
Solution
Let's find the Highest Common Factor (HCF) of the given expressions:
Expression for :
Expression for :
Steps:
-
Identify common prime factors:
- and share the common prime factors 5 and 13.
-
Take the lowest powers of the common factors:
- For , the powers are in and in . The lowest power is .
- For , both have . The lowest power is .
-
HCF in index form:
Thus, the HCF is .
Would you like further details or explanations on any part of this? Here are some additional questions you might consider:
- How do you find the HCF of algebraic expressions with multiple variables?
- What happens if there are no common factors between two expressions?
- Can the HCF include non-prime factors in certain cases?
- How does the HCF differ from the least common multiple (LCM)?
- How would you express the solution if and had more terms or variables?
Tip: Always remember to compare the lowest powers of each common factor when calculating the HCF of two expressions.
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Math Problem Analysis
Mathematical Concepts
Number Theory
Prime Factorization
Highest Common Factor (HCF)
Indices
Formulas
HCF = product of lowest powers of common factors
Theorems
Fundamental Theorem of Arithmetic
Suitable Grade Level
Grades 8-10