This question is driving me crazy. Any insight would be greatly appreciated.

Two old friends met in the park and decided to have a chat. They made themselves comfortable on a bench and started talking: - How are you, old friend? It's already five years since we last saw each other. - I am fine, yeah, you do not know then? I got married since we last met, have two sons already. - Wow, how old are they? - Well, if you multiply their full years, it will be equal to the number of pigeons next to this bench. - Hmm, I need another clue... - Oh, yeah, the eldest looks like his mother... - Oh, I get it now. What are the ages of the two children?
1 and 4.

1, see all possibilities with ages: 1 * 1, 1 * 2, 1*3....
2, take out numbers that would prove that they are same age. One is older than the other so it cannot be: 1 * 1 = 1, 2 * 2 = 4