#MMBLTutorial
Math Tip of the Day:
How to find the GCF(greatest common factor) of string of 1's or string of any numbers:
GCF(m 1's and n 1's) = GCF(m,n) -> Corresponds to the number of 1's.
Example:
1. Find the GCF of 1111... (45 1's) and 1111... (40 1's)
Solution:
Step 1: m = 45, n = 40
Step 2: Get the GCF of 45 and 40.
How to get again the GCF?
a. Prime Factorization of the Numbers
b. Multiply the common factors of the numbers (lowest exponent)
45 = 3^2 * 5
40 = 2^3 * 5
Common = 5
There 5 corresponds to the number 1's
Thus GCF = 11111.
2. Find the GCF of 1111... (2016 1's) and 1111... (108 1's).
Solution:
Step 1: m = 2016, n = 108
Step 2: GCF (2016, 108)
2016 = 2^5 * 3^2 * 7
108 = 2^2 * 3^3
GCF = 2^2 * 3^2 = 4*9 = 36 -> Number of 1's
Therefore, GCF = 1111... (36 1's).
Try the below examples
1. GCF of 333... ( 12 3's) and 333... (18 3's)
2. GCF of 111... ( 400 1's) and 111... (192 1's)
Credits by: Isaiah James Maling 2017
1. 12 and 18
18=12 (1) + 6
12=6 (2) +0
GCF = 6 3'S
2. 400 and 192
400= 192 (2) + 16
192= 16 (12)+0
GCF= 16 1'S
