What Makes a Number Prime?
Exactly two factors — no more, no less.
↳ A prime has exactly two factors: 1 and itself — that single rule defines the entire set.
Kit Library / Mathematics / Number Theory
⚡ Topic Learning KitPrime Numbers Between 1 and 100
English 17 leveled MCQs 58 flashcards 9 games Free
Shared by a Veda learner · Generated with Veda AI
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🎯 Exam Tip
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The whole idea, one bite at a time
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There Are Exactly 25 Primes Below 100
25 primes hide between 1 and 100.
The complete list of primes from 1 to 100 contains exactly 25 numbers — a fact worth memorizing for exams and quick checks.
↳ Memorize the 25 primes in decade blocks — it makes recall far easier than one long list.
The Full List of 25 Primes (Memorize This)
Chant them in groups of four.
↳ Chunk the 25 primes into decade groups — recall becomes rhythmic and reliable.
How to Test if a Number Is Prime
Only check up to the square root.
↳ Testing only primes up to $\sqrt{n}$ is the fastest reliable primality check by hand.
1 Is NOT a Prime Number
The classic trap — 1 is not prime.
↳ Exclude 1 from any prime list — it has only one factor, not two.
2 Is the Only Even Prime
One even prime — just one.
Every even number greater than 2 is divisible by 2, so it has at least three factors (1, 2, itself). That makes 2 the only even prime in the entire number system.
↳ 2 is the unique even prime — every other prime is odd, but not every odd number is prime.
Quick Divisibility Rules to Spot Composites
Three rules filter out most composites.
↳ Divisibility rules for 2, 3, 5, and 11 quickly filter out most composites before deeper testing.
The Largest Prime Below 100
97 is the last one before 100.
97 is the largest prime less than 100. Its only factors are 1 and 97 — and since $\sqrt{97} \approx 9.8$, checking primes 2, 3, 5, 7 is enough to confirm it.
↳ 97 is the largest prime under 100 — the final entry in the 25-prime list.
Exam Tip: Count Primes in a Range Fast
Use decade blocks to count quickly.
↳ Count primes by decade blocks and always verify candidates ending in 1, 3, 7, 9.
Why Primes Matter in Real Life
Your bank login depends on primes.
Prime numbers are not just exam material — they power modern digital security and data systems.
↳ Primes are the backbone of digital security — every secure online transaction relies on them.
Using Primes to Simplify Fractions
Prime factors simplify fractions instantly.
↳ Prime factorization is the cleanest way to simplify fractions and find GCD/LCM.
Prime vs Composite: Side by Side
Two factors vs many factors.
↳ Prime = exactly two factors; composite = more than two. 1 belongs to neither group.
Primes Never Run Out
There is no largest prime — ever.
Euclid proved over 2,000 years ago that there are infinitely many primes. No matter how large a prime you find, there is always a bigger one.
↳ The list of primes is infinite — the 25 below 100 are only the first handful.
Twin Primes and Prime Gaps
Some primes are just two apart.
↳ Twin primes differ by 2; prime gaps measure spacing — both reveal patterns in the prime sequence.
Picture the Primes on a Number Line
See the primes — spot the gaps.
Imagine a number line from 1 to 100 with only the 25 primes marked. You'll notice they thin out as numbers grow — a visual hint that primes become rarer at higher values.
↳ Primes get sparser as numbers grow — density drops from 4 per decade to just 1 near 100.
Smart notes
1
What you'll study, topic by topic
Prime Numbers Between 1 and 100
15 minPrime numbers are natural numbers greater than 1 with exactly two factors: 1 and themselves. Between 1 and 100 there are exactly 25 primes, and knowing them fluently is a foundational skill for factoring, fractions, and…
- A prime number is a whole number greater than 1 with exactly two factors: 1 and itself.
- 1 is neither prime nor composite because it has only one factor.
- 2 is the only even prime number; all other primes are odd.
Full explanation, worked examples & memory tricks in the app
Leveled MCQ practice
Try the smart MCQs from this kit
All 17 questions, laddered from warm-up to topper-level, each with its answer and the reasoning behind it.
Warm-up · 5 questions
Q1. Which of the following is the definition of a prime number?
Beginner
A
Any odd number greater than 1.
B
Any number that cannot be divided by 2.
C
A whole number greater than 1 with exactly two factors: 1 and itself.
D
A whole number greater than 1 with more than two factors.
Show the answer
C · A whole number greater than 1 with exactly two factors: 1 and itself.
A prime number has exactly two distinct factors: 1 and itself. Having more than two factors makes a number composite, and not all odd numbers are prime (e.g., 9, 15).
Q2. Which of the following numbers is NOT prime?
Beginner
A
2
B
9
C
3
D
7
Show the answer
B · 9
9 = 3 × 3, so it has three factors (1, 3, 9) and is composite. 2, 3, and 7 each have exactly two factors.
Q3. How many prime numbers are there between 1 and 100?
Beginner
A
27
B
23
C
21
D
25
Show the answer
D · 25
There are exactly 25 primes between 1 and 100, from 2 up to 97. This is written as π(100) = 25.
Q4. Is 1 a prime number?
Beginner
A
No, because it is an odd number.
B
No, because it has only one factor, not exactly two.
C
Yes, because it is the smallest whole number.
D
Yes, because it is only divisible by 1 and itself.
Show the answer
B · No, because it has only one factor, not exactly two.
1 has only one factor (itself), so it does not meet the definition of a prime number, which requires exactly two distinct factors. 1 is neither prime nor composite.
Q5. There are exactly 25 prime numbers between 1 and 100.
Beginner
A
True
B
False
Show the answer
A · True
There are exactly 25 prime numbers between 1 and 100.
Building up · 7 questions
Q6. A student says, 'All odd numbers are prime.' Which of the following numbers disproves this statement?
Intermediate
A
11
B
13
C
15
D
17
Show the answer
C · 15
15 is odd but composite (15 = 3 × 5), so it has more than two factors. 11, 13, and 17 are all prime, so they do not disprove the statement.
Q7. To test whether a number under 100 is prime, which set of primes is sufficient to check for divisibility?
Intermediate
A
All primes less than 100
B
2, 3, 5, and 7
C
2 and 3 only
D
2, 3, 5, 7, and 11
Show the answer
B · 2, 3, 5, and 7
Since √100 = 10, you only need to test primes up to 10, which are 2, 3, 5, and 7. If none divide the number evenly, it is prime.
Q8. A number under 100 is not divisible by 2, 3, 5, or 7. What can you conclude?
Intermediate
A
The number is definitely composite.
B
The number is even.
C
The number is definitely prime.
D
The number is 1.
Show the answer
C · The number is definitely prime.
If a number under 100 has no prime factor among 2, 3, 5, and 7, then it has no prime factor ≤ √100 = 10, so it must be prime.
Q9. Which of the following numbers is composite?
Intermediate
A
83
B
91
C
89
D
97
Show the answer
B · 91
91 = 7 × 13, so it is composite. 97, 89, and 83 are all prime (none is divisible by 2, 3, 5, or 7).
Q10. Which pair of numbers are twin primes?
Intermediate
A
(13, 17)
B
(7, 11)
C
(3, 5)
D
(2, 3)
Show the answer
C · (3, 5)
Twin primes differ by 2. (3, 5) differ by 2 and are both prime. (2, 3) differ by 1, (7, 11) by 4, and (13, 17) by 4.
Q11. Which of the following is the prime factorization of 84?
Intermediate
A
$4 \times 21$
B
$2^2 \times 3 \times 7$
C
$2 \times 3 \times 14$
D
$2^3 \times 3 \times 7$
Show the answer
B · $2^2 \times 3 \times 7$
84 = 4 × 21 = 2² × 3 × 7. The other options either contain composite factors (14, 4, 21) or give the wrong product (2³ × 3 × 7 = 168).
Q12. A student lists the primes under 20 as: 2, 3, 5, 7, 9, 11, 13, 17, 19. What is the error?
Intermediate
A
The list is correct as written.
B
9 should not be in the list because 9 = 3 × 3.
C
2 should not be in the list because it is even.
D
11 should not be in the list because it is odd.
Show the answer
B · 9 should not be in the list because 9 = 3 × 3.
9 is composite (9 = 3 × 3), so it should not appear in a list of primes. The correct primes under 20 are 2, 3, 5, 7, 11, 13, 17, 19.
Topper level · 5 questions
Q13. Which of the following statements about the Sieve of Eratosthenes is correct?
Advanced
A
You cross out multiples of each prime starting from 2, and the remaining numbers are prime.
B
You test each number by dividing it by every number from 2 to 100.
C
You circle every odd number and cross out the even numbers.
D
You only need to cross out multiples of 2 and 3 to find all primes under 100.
Show the answer
A · You cross out multiples of each prime starting from 2, and the remaining numbers are prime.
The sieve works by crossing out multiples of each prime (2, 3, 5, 7) in turn; the numbers left uncrossed are prime. Crossing out only multiples of 2 and 3 would leave composites like 25 and 49.
Q14. Which of the following numbers is prime?
Advanced
A
87
B
91
C
97
D
99
Show the answer
C · 97
97 is prime (not divisible by 2, 3, 5, or 7). 87 = 3 × 29, 91 = 7 × 13, and 99 = 9 × 11 are all composite.
Q15. A number between 50 and 60 is prime. Which of the following could it be?
Advanced
A
53
B
55
C
51
D
57
Show the answer
A · 53
53 is prime. 51 = 3 × 17, 57 = 3 × 19, and 55 = 5 × 11 are all composite.
Q16. Which of the following statements is TRUE about the density of primes between 1 and 100?
Advanced
A
There are no primes between 90 and 100.
B
The number of primes is the same in both halves.
C
There are more primes between 50 and 100 than between 1 and 50.
D
There are more primes between 1 and 50 than between 50 and 100.
Show the answer
D · There are more primes between 1 and 50 than between 50 and 100.
There are 15 primes between 1 and 50, but only 10 between 50 and 100. Primes become less frequent as numbers increase, though 97 is prime between 90 and 100.
Q17. If you apply the Sieve of Eratosthenes to find all prime numbers between 1 and 100, which of the following numbers will be the last prime number you circle?
Advanced
A
79
B
97
C
83
D
89
Show the answer
B · 97
The last prime number circled when using the Sieve of Eratosthenes up to 100 is 97, as it is the largest prime number in that range. All numbers greater than 97 are either composite or exceed 100.
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