What is the GCF of 35 and 50?

Understand the Problem

The question is asking for the greatest common factor (GCF) of the numbers 35 and 50. To solve this, we need to find the factors of both numbers and identify the largest factor they share.

Answer

$5$

Steps to Solve

List the factors of 35

The factors of 35 are the numbers that divide 35 without leaving a remainder. The factors are:
1, 5, 7, and 35.

So, the list of factors of 35 is:
{1, 5, 7, 35}.

List the factors of 50

Next, we find the factors of 50. The factors are:
1, 2, 5, 10, 25, and 50.

So, the list of factors of 50 is:
{1, 2, 5, 10, 25, 50}.

Identify the common factors

Now, we compare the factors of both numbers to find the common factors. The common factors between 35 and 50 are:
1 and 5.

Determine the greatest common factor

From the common factors {1, 5}, the largest one is 5. Therefore, the greatest common factor (GCF) of 35 and 50 is:
$$ GCF(35, 50) = 5 $$.

The greatest common factor of 35 and 50 is $5$.

More Information

The greatest common factor is useful in simplifying fractions and finding common denominators. Knowing the GCF can also help in solving problems involving ratios and divisibility.

Tips

A common mistake is to include numbers that are not factors of both numbers. Always check if the number divides both original numbers with no remainder.
Another mistake can be to forget to list all factors or to skip numbers while counting. Take your time listing all potential factors.

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