You can use Guass Formula to find the sum from 1 through n .
(n+1)*n/2=141*140/2=141*70
Since we want to find the prime factors:
141=3*47
70=7*2*5
SO we need the greatest which is \(\left [ 47 \right ]\)
You could do complementary counting and see the ones that are not right.
1,2
1,3
2,1
And since the total ways are 25:
1(Because 25/25=1)-3/25(That are wrong)=22/25
Hope This Helps