What is the GCF of 86 and 42?

Understand the Problem

The question is asking for the greatest common factor (GCF) of the numbers 86 and 42. To solve this, we will determine the factors of both numbers and identify the largest factor they share.

Answer

The GCF of 86 and 42 is $2$.

Steps to Solve

List the Factors of 86

To find the factors of 86, we can divide it by each number starting from 1 up to 86. The factors are:

1
2 (since $86 \div 2 = 43$)
43 (since $86 \div 43 = 2$)
86 (since $86 \div 86 = 1$)

So, the factors of 86 are: 1, 2, 43, 86.

List the Factors of 42

Next, we find the factors of 42 in a similar fashion. The factors are:

1
2 (since $42 \div 2 = 21$)
3 (since $42 \div 3 = 14$)
6 (since $42 \div 6 = 7$)
7 (since $42 \div 7 = 6$)
14 (since $42 \div 14 = 3$)
21 (since $42 \div 21 = 2$)
42 (since $42 \div 42 = 1$)

So, the factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.

Identify the Common Factors

Now, we find the common factors of 86 and 42 by comparing their lists:

Common factors: 1 and 2.

Determine the Greatest Common Factor (GCF)

From the common factors, the greatest one is:

The GCF of 86 and 42 is 2.

The greatest common factor (GCF) of 86 and 42 is (2).

More Information

The greatest common factor is useful in simplifying fractions, finding common denominators, and solving problems involving divisibility. The GCF is the largest number that divides both numbers without leaving a remainder.

Tips

Overlooking common factors could lead to a wrong calculation of the GCF. Always ensure to list out all factors clearly.
Confusing GCF with least common multiple (LCM). Remember, GCF finds the largest shared factor, while LCM finds the smallest shared multiple.

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