Generates two non-prime list numbers. First one without answers for my child, the second one with answers for me.

GenerateNumbers.java

package me.asaushkin.desing.classes.collection;

import java.util.*;
import java.util.concurrent.ThreadLocalRandom;
import java.util.stream.Collectors;

public class GenerateNumbers {

    static Queue<Integer> factorizeNumber(Integer num) {
        Queue<Integer> queue = new ArrayDeque<>();
        for (int i = 2; Math.pow(i, 2) < num; i++) {
            if (num % i == 0) {
                queue.offer(i);
                num = num / i;
                i = 1;
            }
        }
        queue.offer(num);
        return queue;
    }


    static final int MAX_PRIME = 11;

    public static void main(String[] args) {
        Map<Integer, Queue<Integer>> result = new HashMap<>();
        while (result.size() < 10) {
            Integer nextInt = ThreadLocalRandom.current().nextInt(100, 1000);
            Queue<Integer> factorQueue = factorizeNumber(nextInt);

            if (factorQueue.stream().noneMatch(s -> s > MAX_PRIME))
                result.put(nextInt, factorQueue);
        }

        System.out.println(result.entrySet().stream().
                peek(m -> System.out.println(m.getKey() + ": " + m.getValue())).
                map(e -> e.getKey()).
                collect(Collectors.toList())
        );
    }
}

Generates output like this:

144: [2, 2, 2, 2, 9]
224: [2, 2, 2, 2, 2, 7]
324: [2, 2, 3, 3, 9]
693: [3, 3, 7, 11]
135: [3, 3, 3, 5]
840: [2, 2, 2, 3, 5, 7]
539: [7, 7, 11]
189: [3, 3, 3, 7]
126: [2, 3, 3, 7]
495: [3, 3, 5, 11]
[144, 224, 324, 693, 135, 840, 539, 189, 126, 495]