For all the answers I will assume that all buttons both green and blue must be used.
For the first question we will start by searching all the divisors of 16;
16: 1, 2, 4, 8, 16 We will think about the numbers of green buttons that can be used as the divisors of 16. We will check if t<span>he dividend of 16 to its divisors is a divisor for 56. </span> 1 => 16 vests with 1 green button 56/16 = 3.5 2=> 8 vests with 2 green buttons 56/8 = 7 4=> 4 vests with 4 green buttons 56/4 = 14 8=> 2 vests with 8 green buttons 56/2 = 28 16=> 1 vest with 16 green buttons 56/1 = 56
From all the above results we concluded that Lee can make: 8 vests with 2 green buttons and 7 blue buttons 4 vests with 4 green buttons and 14 blue buttons 2 vests with 8 green buttons and 28 blue buttons 1 vest with 16 green buttons and 56 blue buttons
For the second question, the <span>greatest number of vests represents the greatest common divider of 16 and 56. </span>First, we break into prime factors 16 = 2^4 56 = 2^3 *7 The greatest common divider is 8. <span>Lee can make 8 vests and each one will have 2 green buttons and 7 blue buttons (16/8=2 and 56/8=7)</span>
