Explanation:
the easiest way is to find the prime factors of every number :
15 ÷ 2 no, next possible prime factor
15 ÷ 3 = 5
5 ÷ 3 no, next possible prime factor
5 ÷ 5 = 1 finished
so, 15 = 3×5
45 ÷ 2 no, next possible prime factor
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 3 no, next possible prime factor
5 ÷ 5 = 1 finished
so, 45 = 3×3×5
30 ÷ 2 = 15
15 ÷ 2 no, next possible prime factor
15 ÷ 3 = 5
5 ÷ 3 no, next possible prime factor
5 ÷ 5 = 1 finished
so, 30 = 2×3×5
the greatest common factor is the largest number all 3 numbers can be divided by without remainder.
we get this as the product of all prime factors they have in common.
we see, all three numbers have one 3 and one 5 factor in common.
so, the greatest common factor is 3×5 = 15.