AHGSIGMA

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