How do you find the greatest common factor of 88, 66?

Question

Riley Anderson · Accepted Answer

#GCF(66,88)=22#

make a list of every factor affecting the two numbers, look for those that are shared, and select the biggest one.

factors 66:#{1,2,3,6,11,22,33,66}# factors 88:#{1,2,4,8,11,22,44,88}#

common factors:#{1,2,3,6,11,22,33,66}nn{1,2,4,8,11,22,44,88}#

#{1,2,11,22}#

#GCF(66,88)=22#

Jeremiah Andrews · Answer

#GCF (88, 66) = 22#, but there is another way to calculate it, sometimes more usefull...

Calculate the #GCF# making a list of the factors of numbers and looking for the biggest of those who are repeated is a simple method but it can be very slow to use if we have more than two numbers and they are of a large size. Instead, using the other method I describe below, you can calculate the #GCF# fairly quickly, whatever numbers we have to consider, and the strategy used also serves to other operations and related integer calculations (eg , calculating the #LCM#, simplifying radicals or fractions ...). (1) For each of the numbers that we have to consider, we make its prime factorization: #color(white) "0000"#For example, suppose you want to find the #GCF# of #600#, #1500# #color(white) "0000"#and #3300#. The factorization of these three numbers is: #color(white) "00000000000000000000" 600 = 2^3 cdot 3 cdot 5^2# #color(white) "0000000000000000000" 1500 = 2^2 cdot 3 cdot 5^3# #color(white) "0000000000000000000" 3300 = 2^2 cdot 3 cdot 5^2 cdot 11# (2) We chose those factors that are repeated in all numbers, first taking the base of each. #color(white) "0000"#In our example, as the powers with equal bases on the three #color(white) "0000"#numbers are those with base 2, 3 and 5, those would be the #color(white) "0000"#factors to consider. The factor 11, however, only appears in the #color(white) "0000"#decomposition of one of the numbers, so we discard it: #color(white) "000000000000" GCF (600, 1500, 3300) = 2^? cdot 3^? cdot 5^?# (3) We must use as exponents, for each base, the smallest of which appear in the prime factorization. #color(white) "0000"#Of all the factors that have #2# as a base, the smallest exponent #color(white) "0000"#that appears is the #2#, therefore, we will use #2^2# in calculating the #color(white) "0000" GCF#. We do the same with the #3# (which is raised to #1# in the #color(white) "0000"#three numbers, so we'll use #3^1#) and #5# (which has the smallest #color(white) "0000"#exponent #2#): #color(white) "000000000000" GCF (600, 1500, 3300) = 2^2 cdot 3 cdot 5^2 = 300#. We can recall the method of calculating the #GCF# learning that "we take only those factors that are repeated, and using the smallest possible exponent". More abbreviated form: #color(white) "0000" GCF = "common factors with lower exponent"#.

Zoe Adams · Answer

undefined To find the greatest common factor (GCF) of 88 and 66, you can use the method of prime factorization.

1. Begin by finding the prime factorization of each number:
   - 88 = 2^3 * 11
   - 66 = 2 * 3 * 11

2. Identify the common prime factors: 2 and 11.

3. Multiply these common prime factors together: 
   GCF = 2 * 11 = 22.

So, the greatest common factor of 88 and 66 is 22.