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Quiz about Do You Know Your Divisibilities

Do You Know Your Divisibilities? Quiz

Are you able to figure out if a number is divisible by another just by looking at it? Let's find out.

A multiple-choice quiz by nsalem. Estimated time: 3 mins.

Author
nsalem

Time
3 mins

Type
Multiple Choice

Quiz #
351,287

Updated
Jul 23 22

# Qns
10

Difficulty
Average

Avg Score
7 / 10

Plays
410

One at a Time - Single Page - Timed Game

Question 1 of 10

1. Let's start with the easiest rule. Is 523232856624654242125 divisible by 2?

Yes

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Question 2 of 10

2. Which of the following choices for p would make 223232p4 NOT divisible by 4? Hint

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Question 3 of 10

3. How many of the last digits do you have to test to find out if a number is divisible by 8? Hint

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Question 4 of 10

4. Is the number 2322323245665 divisible by 5?

Yes

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Question 5 of 10

5. What four digits could replace p to make 22p5 divisible by 3? Hint

1,2,4 or 7

0,3,6 or 9

2,3,5 or 8

1,3,6 or 9

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Question 6 of 10

6. What is the only digit to replace q that can make 121228q9 divisible by 9 ? Hint

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Question 7 of 10

7. A number is divisible by 13 if and only if the sum of every other digit is subtracted that from the sum of all the remaining digits the results have to be divisible by 13 only.

True

False

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Question 8 of 10

8. Is it possible to tell if a number is divisible by 7 without doing the division?

Yes

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Question 9 of 10

9. Now that we know the rules for many of the numbers lets see if you can get two digits. 2315pq is divisible by 5 and 8. What is one version of p? What is q? Hint

p=2 and q=5

p=6 and q=0

p=2 and q=3

p=5 and q=0

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Question 10 of 10

10. 247p743q6 is divisible by 11 and 8. What else is it divisible by? Hint

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Most Recent Scores

Dec 18 2024 : emmal2000uk: 2/10
Nov 28 2024 : andymuenz: 9/10

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Quiz Answer Key and Fun Facts

1. Let's start with the easiest rule. Is 523232856624654242125 divisible by 2?

Answer: No

When checking to see if a number is divisible by 2 you check the last digit. The way to look at it is 2 to the first power makes it require the last digit.

2. Which of the following choices for p would make 223232p4 NOT divisible by 4?

Answer: 1

Because 4 is 2 squared, the last 2 digits of the number have to be divisible by 4 for the whole thing to be divisible by 4.

3. How many of the last digits do you have to test to find out if a number is divisible by 8?

Answer: 3

8 = 2 to the 3rd power; therefore, the last 3 digits have to be divisible by 8 for the entire number to be divisible by 8. If you want to know if a number is divisible by a 2 to the power of p, just test the last p digits.

4. Is the number 2322323245665 divisible by 5?

Answer: Yes

Any number that ends in 5 or 0 is divisible by 5.

5. What four digits could replace p to make 22p5 divisible by 3?

Answer: 0,3,6 or 9

To tell if a number is divisible by 3, you need to sum the digits, and if the sum of the digits are divisible by 3 than the entire number is divisible by 3.

6. What is the only digit to replace q that can make 121228q9 divisible by 9 ?

Answer: 2

When testing to see if a number is divisible by nine, you use the same technique as for three only the sum of the digits has to be divisible by 9.

7. A number is divisible by 13 if and only if the sum of every other digit is subtracted that from the sum of all the remaining digits the results have to be divisible by 13 only.

Answer: false

This method works for a divider of eleven, not thirteen. Also it works if the results equal 0. 44 equals 11 * 4 so it is divisible by 11 but 4-4 = 0, so the rule has to include 0. 52789 = 4799*11 the 5+7+9 = 21 2+8 = 10 21-10 = 11 therefore it has to be divisible by 11 by this rule. I haven't heard of a rule for 13 yet.

8. Is it possible to tell if a number is divisible by 7 without doing the division?

Answer: Yes

The method I know is taking every other three digits and summing them and subtracting from the remaining digits and if that's divisible by 7 it's divisible by 7. The problem is it only works for a minimum of 4 digit number, and it's easier to just do the division. One example is 1701 is divisible by 7 because 701-1= 700 and 700 is divisible by 7 so the number is divisible by 7.

9. Now that we know the rules for many of the numbers lets see if you can get two digits. 2315pq is divisible by 5 and 8. What is one version of p? What is q?

Answer: p=6 and q=0

For the number to be even and divisible by 5 q has to be 0. The last three digits have to be divisible by 8 for the entire number to be. One step at a time makes this problem easy.

10. 247p743q6 is divisible by 11 and 8. What else is it divisible by?

Answer: 3

To start this problem you need to find out what q could be using the 8 rule (getting 3 or 7) and then p using the 11 rule (which gives 3 if q=3 but 10 - an impossible value - if q=7).

By the way, If both 9 and 3 are dividers in a multiple choice question with only one correct answer, 9 is automatically ruled out. 9 is 3 squared so anything divisible by 9 is also divisible by 3. This question was similar to a question I had in college when I was practicing for a math contest.

Source: Author nsalem

This quiz was reviewed by FunTrivia editor WesleyCrusher before going online.
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