+0

# Help On Complex Numbers

+1
714
5
+141

The four consecutive digits a, b, c and d are used to form the four-digit numbers abcd and dcba. What is the greatest common divisor of all numbers of the form abcd+dcba?

Jun 12, 2019

#3
+9180
+4

1234  +  4321   =   5555

2345  +  5432   =   7777

3456  +  6543   =   9999

4567  +  7654   =   12221

5678  +  8765   =   14443

6789  +  9876   =   16665

And....

 5555 _=_ 101 * 11 * 5 7777 = 101 * 11 * 7 9999 = 101 * 11 * 3 * 3 12221 = 101 * 11 * 11 14443 = 101 * 11 * 13 16665 = 101 * 11 * 3 * 5

gcd(5555, 7777, 9999, 12221, 14443, 16665)  =  101 * 11  =  1111

Jun 13, 2019

#1
-3

The greatest GCD of abcd and dcba is when they total 9999 when added together. So:

3456 and 6543 have a GCD of 9.

Jun 13, 2019
#2
+141
+1

That's incorrect, sorry.

Jun 13, 2019
#3
+9180
+4

1234  +  4321   =   5555

2345  +  5432   =   7777

3456  +  6543   =   9999

4567  +  7654   =   12221

5678  +  8765   =   14443

6789  +  9876   =   16665

And....

 5555 _=_ 101 * 11 * 5 7777 = 101 * 11 * 7 9999 = 101 * 11 * 3 * 3 12221 = 101 * 11 * 11 14443 = 101 * 11 * 13 16665 = 101 * 11 * 3 * 5

gcd(5555, 7777, 9999, 12221, 14443, 16665)  =  101 * 11  =  1111

hectictar Jun 13, 2019
#4
+114139
+4

Nice, hectictar   !!!!

CPhill  Jun 13, 2019
#5
+141
+2

Thanks so much!

Jun 13, 2019