Smallest Multiple
$2520$ is the smallest number that can be divided by each of the numbers from $1$ to $10$ without any remainder. What is the smallest positive number...
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John Rhodes
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August 15, 2023
Largest Palindrome Product
A palindromic number reads the same both ways. The largest palindrome made from the product of two $2$-digit numbers is $9009 = 91 \times 99$. Find the...
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John Rhodes
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August 15, 2023
Largest Prime Factor
The prime factors of $13195$ are $5, 7, 13$ and $29$. What is the largest prime factor of the number $600851475143$? We can find the largest prime...
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John Rhodes
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August 15, 2023
Even Fibonacci Numbers
Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with $1$ and $2$, the first $10$ terms will be:...
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John Rhodes
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August 15, 2023
Multiples of $3$ or $5$
If we list all the natural numbers below $10$ that are multiples of $3$ or $5$, we get $3, 5, 6$ and $9$. The sum of these...
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John Rhodes
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July 31, 2023
Preserving Row Echelon Form | The Impact of Elementary Row Operations on Matrices
If an elementary row op is applied to a matrix that is in row echelon form, the resulting matrix will still be in row echelon form. Yes,...
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John Rhodes
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July 31, 2023
Why Every Matrix Has a Unique Row Echelon Form | Defining and Proving the Uniqueness of Matrix Forms
Every matrix has a unique row echelon form. To understand why every matrix has a unique row echelon form, we need to clarify the definitions of a...
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John Rhodes
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July 31, 2023
Finding x-intercepts | A step-by-step guide and examples for finding the points where a function intersects the x-axis.
x-intercepts of f(x) The x-intercepts of a function f(x) are the points where the graph of the function intersects the x-axis The x-intercepts of a function f(x)...