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Questions and Answers
Express the number 72 as a product of its prime factors in index notation.
Express the number 72 as a product of its prime factors in index notation.
$2^3 \times 3^2$
Determine the Highest Common Factor (HCF) of $2^3 \times 3^2 \times 5$ and $2^2 \times 3^3 \times 7$.
Determine the Highest Common Factor (HCF) of $2^3 \times 3^2 \times 5$ and $2^2 \times 3^3 \times 7$.
$2^2 \times 3^2 = 36$
Find the Least Common Multiple (LCM) of 16 and 24 using their prime factorizations.
Find the Least Common Multiple (LCM) of 16 and 24 using their prime factorizations.
48
Simplify the following expression using the laws of indices: $\frac{(3^4 \times 3^{-2})^3}{3^5}$
Simplify the following expression using the laws of indices: $\frac{(3^4 \times 3^{-2})^3}{3^5}$
Evaluate the expression: $(2^0 + 3^{-1}) \times 3^2$.
Evaluate the expression: $(2^0 + 3^{-1}) \times 3^2$.
Numbers $A$ and $B$ have prime factorizations $A = 2^4 \times 3 \times 5^2$ and $B = 2 \times 3^2 \times 7$. What is the least common multiple (LCM) of $A$ and $B$?
Numbers $A$ and $B$ have prime factorizations $A = 2^4 \times 3 \times 5^2$ and $B = 2 \times 3^2 \times 7$. What is the least common multiple (LCM) of $A$ and $B$?
Without fully calculating, explain whether the HCF of two numbers can ever be larger than the smallest of the two numbers. Why or why not?
Without fully calculating, explain whether the HCF of two numbers can ever be larger than the smallest of the two numbers. Why or why not?
Find the prime factors of 924.
Find the prime factors of 924.
What is the smallest number that has 2, 3, 5, and 7 as its only prime factors?
What is the smallest number that has 2, 3, 5, and 7 as its only prime factors?
The LCM of two numbers is 120 and their HCF is 4. If one of the numbers is 24, what is the other number?
The LCM of two numbers is 120 and their HCF is 4. If one of the numbers is 24, what is the other number?
Express 360 as a product of its prime factors in index notation.
Express 360 as a product of its prime factors in index notation.
Explain how finding the prime factors of two numbers helps in determining their HCF and LCM.
Explain how finding the prime factors of two numbers helps in determining their HCF and LCM.
Flashcards
Index Notation
Index Notation
A way of writing repeated multiplication of the same number using a base and an exponent.
Product of Powers
Product of Powers
When multiplying powers with the same base, add the exponents: a^m * a^n = a^(m+n)
Quotient of Powers
Quotient of Powers
When dividing powers with the same base, subtract the exponents: a^m / a^n = a^(m-n)
Power of a Power
Power of a Power
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Zero Exponent
Zero Exponent
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What is LCM?
What is LCM?
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What is HCF?
What is HCF?
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What is Prime Factorization?
What is Prime Factorization?
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How to find LCM using Prime Factorization?
How to find LCM using Prime Factorization?
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How to find HCF using Prime Factorization?
How to find HCF using Prime Factorization?
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What is a Prime Factor?
What is a Prime Factor?
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What is a Prime Number?
What is a Prime Number?
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How to find Prime Factors?
How to find Prime Factors?
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