In best widespread issue, discovering the best widespread issue of numbers was the purpose. On this lesson, we’ll do the identical factor, however we’ll take the idea to the following stage by in search of the best widespread issue of expressions.

Recall that if we’re in search of the GCF of 12 and 20, we have to first issue every quantity into its prime factorization as proven within the determine under.

As you’ll be able to see, 2 × 2 = 4 is the best issue 12 and 20 have in widespread, so 4 is the GCF of 12 and 20.

Discover the GCF of 12×2 and 20×4

Now, not solely we have to develop 12 and 20 into their prime factorizations, we additionally must do the identical for x2 and x4 as demonstrated within the determine above.

As you’ll be able to see from the determine above, the GCF of 12×2 and 20×4 is 2 × 2 × x × x = 4×2

Just a few extra examples exhibiting how discovering the best widespread issue of expressions work

Instance #1

Discover the GCF of 15×4, 25×3, and 75×5

First check out the determine under and study it fastidiously.

common factor of  15x^4, 25x^3, and 75x^5

Thus, the GCF for 15×4, 25×3, and 75×5 is 5 × x × x × x = 5×3

There’s a quicker method to discover the best widespread issue of an expression.

When there are a lot of exponential expressions which have the identical variable or similar quantity as base, the best widespread issue is the expression with the smallest exponent.

For instance, the best widespread issue of x4, x3, and x5 is x3 since x3 is the expression with the smallest exponent. By the identical token, the best widespread issue of 32, 34, and 33 is 32 since 32 is the expression with the smallest exponent.

Instance #2

Discover the GCF of w3 + w2 + w 

We will break down this trinomial into three separate expressions: w3, w2, and w.

Since w is the expression with the smallest exponent, w is the best widespread issue.

Instance #3

Discover the GCF of 4w5 + 8w4 + 16w3

4w5 + 8w4 + 16w3 = 22w5 + 23w4 + 24w3

We will break down this trinomial into three separate expressions: 22w5,23w4,and 24w3

For 22, 23, and 24, the GCF is 22

For w5, w4, and w3, the GCF is w3

Subsequently, the GCF of 4w5 + 8w4 + 16w3 is 22w3 or 4w3

Discovering the best widespread issue quiz. See how effectively you perceive this lesson.

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