How do you find the GCF of 98 and 28?

1 Answer
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

2

This answer has been featured!

Featured answers represent the very best answers the Socratic community can create.

Learn more about featured answers

Nov 8, 2016

Answer:

#14#

Explanation:

Here are a couple of methods:

Method 1 - Division and remainder

To find the GCF of two numbers proceed as follows:

  • Divide the larger number by the smaller to give a quotient and remainder.

  • If the remainder is #0# then the GCF is the smaller number.

  • Otherwise repeat with the smaller number and remainder.

In our example, we find:

#98 / 28 = 3" "# with remainder #14#

#28 / 14 = 2" "# with remainder #0#

So the GCF of #98# and #28# is #14#

Method 2 - Prime factorisation

Factorise #98# and #28# down to their prime factors, and identify the factors which are common - including multiplicity.

#color(white)(00000)98color(white)(0000000000)28#
#color(white)(0000)"/"color(white)(00)"\"color(white)(00000000)"/"color(white)(00)"\"#
#color(white)(000)2color(white)(000)49color(white)(000000)2color(white)(000)14#
#color(white)(000000)"/"color(white)(00)"\"color(white)(00000000)"/"color(white)(00)"\"#
#color(white)(00000)7color(white)(0000)7color(white)(000000)2color(white)(0000)7#

So:

#98 = 2 xx 7 xx 7#

#28 = 2 xx 2 xx 7#

The common factors in the common multiplicities give us the GCF when multiplied:

#"GCF" = 2 xx 7 = 14#

Was this helpful? Let the contributor know!
1500
Impact of this question
Answer impact map
15 views around the world
You can reuse this answer
Creative Commons License