How do you find the GCF of 98 and 28?

Question

Skylar Adams · Accepted Answer

#14#

Here are a few techniques:

Division and remainder in Method 1

Follow these steps to determine the GCF of two numbers:

To find the remainder and quotient, divide the larger number by the smaller one.

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

If not, repeat with the remainder and smaller number.

In our instance, we discover:

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

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

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

Second Method: Prime Factorization

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#

Multiplying the common factors in the common multiplicities yields the GCF:

#"GCF" = 2 xx 7 = 14#

Nova Allen · Answer

undefined To find the Greatest Common Factor (GCF) of 98 and 28, you can use prime factorization:

1. Prime factorize both numbers:
   98 = 2 * 7 * 7
   28 = 2 * 2 * 7

2. Identify the common prime factors: 2 and 7.

3. Multiply the common prime factors together: 2 * 7 = 14.

Therefore, the GCF of 98 and 28 is 14.