Divisibility Shortcuts Quiz: Divisibility Shortcuts for Small Primes

  • 4th Grade
Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7682 | Total Attempts: 9,547,133
| Questions: 20 | Updated: Dec 17, 2025
Please wait...
Question 1 / 20
0 %
0/100
Score 0/100
1) Which number is immediately eliminated as a prime candidate by the divisibility-by-2 test?

Explanation

Any even number greater than 2 is composite. 46 is even, so it’s eliminated by the ×2 test.

Submit
Please wait...
About This Quiz
Divisibility Shortcuts Quiz: Divisibility Shortcuts For Small Primes - Quiz

How can quick divisibility rules help you evaluate numbers without long calculations? In this quiz, you’ll explore shortcuts for small primes, seeing how digit patterns, endings, and sums reveal divisibility instantly. You’ll practice applying these rules to various numbers, compare which shortcut fits which situation, and understand why each trick... see moreworks logically. By the end, you’ll feel comfortable using fast divisibility checks to simplify arithmetic, verify answers, and strengthen number sense.
see less

2) If a number ends with 0 or 5, it is divisible by 5.

Explanation

Ending digit 0 or 5 ⇒ the number is a multiple of 5 by the rule for 5.

Submit
3) Compute the digit sum of 57 (used for the divisibility-by-3 test): ____.

Explanation

Digit sum 5+7 = 12. Since 12 is a multiple of 3, 57 is divisible by 3.

Submit
4) Which of these passes the 2, 3, and 5 tests (so it remains a prime candidate)?

Explanation

49 is not divisible by 2 (odd), 3 (4+9=13 not multiple of 3), or 5 (doesn’t end in 0 or 5). It remains a candidate (though not guaranteed prime).

Submit
5) Select all numbers divisible by 3 (use the digit-sum test).

Explanation

27: 2+7=9 ⇒ ÷3; 42: 4+2=6 ⇒ ÷3; 75: 7+5=12 ⇒ ÷3. 34 and 58 have digit sums 7 and 13, not multiples of 3.

Submit
6) All even numbers greater than 2 are composite.

Explanation

Even numbers >2 have at least factors 2 and n/2, so they are composite.

Submit
7) For 85, the last-digit rule shows it is divisible by ____.

Explanation

Numbers ending in 0 or 5 are divisible by 5. 85 ends in 5.

Submit
8) Using only the divisibility-by-3 test, which number is eliminated?

Explanation

51 has digit sum 5+1=6, a multiple of 3, so 51 is divisible by 3.

Submit
9) Select all numbers ruled out immediately by the 2 or 5 tests.

Explanation

62 and 84 are even ⇒ divisible by 2. 65 and 90 end in 5 or 0 ⇒ divisible by 5. 71 is odd, doesn’t end in 0/5, so not ruled out by 2 or 5.

Submit
10) If a number under 100 is not divisible by 2, 3, or 5, then it must be prime.

Explanation

Passing the 2,3,5 checks only makes it a candidate. Example: 49 passes 2,3,5 but is 7×7 (composite).

Submit
11) Give a number greater than 10 that passes the 2, 3, and 5 tests (a prime candidate): ____.

Explanation

11 is odd, 1+1=2 (not multiple of 3), and doesn’t end with 0 or 5, so it passes the filters.

Submit
12) Which number is divisible by 5?

Explanation

95 ends in 5 ⇒ divisible by 5. Others end in 2,4,7.

Submit
13) Select all numbers whose digit sums are multiples of 3.

Explanation

39: 3+9=12; 66: 6+6=12; 81: 8+1=9. Each digit sum is a multiple of 3, so the numbers are divisible by 3.

Submit
14) Any number ending in 0 is divisible by both 2 and 5.

Explanation

Ending in 0 means even (÷2) and a multiple of 5 (÷5).

Submit
15) The last digit of 246 is ____, so 246 is divisible by 2.

Explanation

A number is divisible by 2 if its last digit is even. 246 ends in 6.

Submit
16) Which number is definitely composite by the 2,3,5 shortcuts?

Explanation

75 ends in 5 (÷5) and 7+5=12 (÷3), so it’s composite. 71,73,79 pass 2,3,5 checks (candidates).

Submit
17) Select all numbers that pass the 2, 3, and 5 checks (they’re candidates only).

Explanation

49,77,91,97 are not divisible by 2,3,5. 65 ends in 5 ⇒ divisible by 5. Note: passing checks doesn’t prove primality.

Submit
18) 2 is prime and is the only even prime.

Explanation

2 has only two factors (1 and 2) and is the sole even prime; all other even numbers are ≥2×something.

Submit
19) Compute the digit sum of 88 to check divisibility by 3: ____.

Explanation

8+8=16, which is not a multiple of 3, so 88 is not divisible by 3.

Submit
20) Which is the smallest number greater than 60 that is divisible by 3?

Explanation

Test by digit sum: 6+3=9 ⇒ multiple of 3. 61 and 62 have sums 7 and 8; 64 has sum 10.

Submit
×
Saved
Thank you for your feedback!
View My Results
Cancel
  • All
    All (20)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
Which number is immediately eliminated as a prime candidate by the...
If a number ends with 0 or 5, it is divisible by 5.
Compute the digit sum of 57 (used for the divisibility-by-3 test):...
Which of these passes the 2, 3, and 5 tests (so it remains a prime...
Select all numbers divisible by 3 (use the digit-sum test).
All even numbers greater than 2 are composite.
For 85, the last-digit rule shows it is divisible by ____.
Using only the divisibility-by-3 test, which number is eliminated?
Select all numbers ruled out immediately by the 2 or 5 tests.
If a number under 100 is not divisible by 2, 3, or 5, then it must be...
Give a number greater than 10 that passes the 2, 3, and 5 tests (a...
Which number is divisible by 5?
Select all numbers whose digit sums are multiples of 3.
Any number ending in 0 is divisible by both 2 and 5.
The last digit of 246 is ____, so 246 is divisible by 2.
Which number is definitely composite by the 2,3,5 shortcuts?
Select all numbers that pass the 2, 3, and 5 checks (they’re...
2 is prime and is the only even prime.
Compute the digit sum of 88 to check divisibility by 3: ____.
Which is the smallest number greater than 60 that is divisible by 3?
Alert!

Advertisement