What is the smallest number which must be subtracted from 68 to make it divisible by 7?

Question

GinnyAnswer · Answer

Test each number from the set (2, 3, 4, 5, 6, 7) by subtracting it from 68. 
 Check if the result is divisible by 7. 
 Find that 68 − 5 = 63 , which is divisible by 7. 
 The smallest number is 5 ​ . 
 
 Explanation 
 
 Problem Analysis We are given the number 68 and a set of numbers (2, 3, 4, 5, 6, 7). Our goal is to find the smallest number from this set that, when subtracted from 68, results in a number divisible by 7. 
 
 Checking Each Number Let's test each number in the set to see if subtracting it from 68 results in a multiple of 7.

If we subtract 2: 68 − 2 = 66 . Is 66 divisible by 7? No, 66 ÷ 7 = 9 with a remainder of 3. 
 If we subtract 3: 68 − 3 = 65 . Is 65 divisible by 7? No, 65 ÷ 7 = 9 with a remainder of 2. 
 If we subtract 4: 68 − 4 = 64 . Is 64 divisible by 7? No, 64 ÷ 7 = 9 with a remainder of 1. 
 If we subtract 5: 68 − 5 = 63 . Is 63 divisible by 7? Yes, 63 ÷ 7 = 9 with no remainder. 
 If we subtract 6: 68 − 6 = 62 . Is 62 divisible by 7? No, 62 ÷ 7 = 8 with a remainder of 6. 
 If we subtract 7: 68 − 7 = 61 . Is 61 divisible by 7? No, 61 ÷ 7 = 8 with a remainder of 5.

Identifying the Smallest Number We found that subtracting 5 from 68 gives us 63, which is divisible by 7. Since we checked the numbers in increasing order, 5 is the smallest number in the set that satisfies the condition. 
 
 Final Answer Therefore, the smallest number that must be subtracted from 68 to make it divisible by 7 is 5.

Examples 
 Imagine you have 68 cookies and want to divide them equally among 7 friends. However, you need to eat some cookies first so that the remaining number is perfectly divisible by 7. By finding the smallest number to subtract (in this case, 5), you ensure that the remaining 63 cookies can be divided equally, giving each friend 9 cookies. This problem demonstrates a practical application of divisibility in everyday scenarios.

Anonymous · Answer

The smallest number that must be subtracted from 68 to make it divisible by 7 is 5. By subtracting 5 from 68, we get 63, which is divisible by 7 with no remainder. There are no smaller numbers that result in a divisible outcome when subtracted from 68. 
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What is the smallest number which must be subtracted from 68 to make it divisible by 7?

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