Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Chapter 5: Problem 6
Use rules of divisibility to determine whether each number given is divisible by a. 2 b. 3 c. 4 d. 5 e. 6 f. 8 g. 9 h. 10 i. 12 . 89,001
Short Answer
Expert verified
The number 89,001 is divisible by 3 and 9.
Step by step solution
01
Testing divisibility by 2
A number is divisible by 2 if its last digit is even. The last digit of 89,001 is 1, which is not even. So 89,001 is not divisible by 2.
02
Testing divisibility by 3
A number is divisible by 3 if the sum of its digits is divisible by 3. For 89,001, the sum of the digits is \(8 + 9 + 0 + 0 + 1 = 18\), which is divisible by 3. So, 89,001 is divisible by 3.
03
Testing divisibility by 4
A number is divisible by 4 if the number formed by its last two digits is divisible by 4. The number formed by the last two digits of 89,001 is 01, which is not divisible by 4. So, 89,001 is not divisible by 4.
04
Testing divisibility by 5
A number is divisible by 5 if its last digit is 0 or 5. The last digit of 89,001 is 1, so 89,001 is not divisible by 5.
05
Testing divisibility by 6
A number is divisible by 6 if it is divisible by both 2 and 3. As we already determined, 89,001 is divisible by 3 but not by 2. Therefore, 89,001 is not divisible by 6.
06
Testing divisibility by 8
A number is divisible by 8 if the number formed by its last three digits is divisible by 8. For 89,001, the last three digits form the number 001, which is not divisible by 8. Therefore, 89,001 is not divisible by 8.
07
Testing divisibility by 9
A number is divisible by 9 if the sum of its digits is divisible by 9. We already found the sum of the digits of 89,001 to be 18, which is divisible by 9. So, 89,001 is divisible by 9.
08
Testing divisibility by 10
A number is divisible by 10 if its last digit is 0. The last digit of 89,001 is 1, so 89,001 is not divisible by 10.
09
Testing divisibility by 12
A number is divisible by 12 if it is divisible by both 3 and 4. We have already determined that 89,001 is divisible by 3 but not by 4, so 89,001 is not divisible by 12.
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with 91影视!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Divisible by 2
To determine if a number is divisible by 2, we need to check if its last digit is an even number. Even numbers are numbers that end with 0, 2, 4, 6, or 8. This rule works because every even number can be perfectly divided by 2, with no remainder left. So, if you are looking at a number and you want to know whether 2 is a factor, just glance at the last digit! If it鈥檚 an even number, then yes, the whole number is divisible by 2. If not, then it's not divisible by 2. For example, the number 46 is divisible by 2 because it ends in 6. In contrast, a number like 89,001 is not divisible by 2 because its last digit is 1, which is not even.
Divisible by 3
A neat trick for finding out if a number is divisible by 3 involves the sum of its digits. You simply add up all the digits in the number, and if that sum can be divided by 3 without leaving a remainder, then the whole number is divisible by 3. This rule is handy because it avoids repetitive long-division calculations. For example, take the number 89,001. You add the digits like this: 8 + 9 + 0 + 0 + 1 to get a total of 18. Since 18 can be divided by 3 (giving a result of 6 with no remainder), the number 89,001 is also divisible by 3.
Divisible by 5
Divisibility by 5 is one of the simplest to figure out, thanks to its particular pattern. Specifically, a number is divisible by 5 if its last digit is either a 0 or a 5. This is because multiples of 5 always end in either a 0 or a 5. Thus, if you check the last digit of any number and it's either one of these two digits, the number as a whole can be exactly divided by 5. For instance, the number 40 satisfies this rule, as it ends in 0. However, a number like 89,001 doesn鈥檛 meet this condition because its last digit, 1, is neither 0 nor 5.
Divisible by 9
Just like with the divisibility rule for 3, the rule for 9 involves adding up the digits of the number. If the sum of the digits is divisible by 9, then the entire number is divisible by 9. This rule helps identify multiples of 9 easily and effectively. Let's apply this to our example number, 89,001. When we add up the digits: 8 + 9 + 0 + 0 + 1, we get 18. Since 18 can be divided by 9 evenly (resulting in 2 with no remainder), this means 89,001 itself is divisible by 9. This trick simplifies what could otherwise be complex calculations into straightforward addition and division.
