The prime factorization of 7429 is 17 × 19 × 23. It is found by dividing 7429 by the smallest prime that divides it (17), then factorising the quotient 437 (= 19 × 23). All three factors — 17, 19, and 23 — are prime numbers, confirming that 7429 is a composite number with exactly three prime factors.
7429 = 17 × 19 × 23 (prime factorization).
7429 is a composite number — it is NOT prime.
Step-by-step: 7429 ÷ 17 = 437; 437 ÷ 19 = 23; 23 is prime.
Verification: 17 × 19 = 323; 323 × 23 = 7,429 ✓
7429 is the product of three consecutive prime numbers: 17, 19, and 23.
7429 has exactly 8 factors: 1, 17, 19, 23, 323, 391, 437, 7429.
The number of factors = (1+1)(1+1)(1+1) = 8, since each prime appears once.
To check if 7429 is prime, test divisibility by all primes up to √7429.
√7429 ≈ 86.2
Primes to test: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83
Quick checks: • Divisible by 2? No — 7429 is odd. • Divisible by 3? Digit sum = 7+4+2+9 = 22; 22 is not divisible by 3. No. • Divisible by 5? Doesn't end in 0 or 5. No. • Divisible by 7? 7429 ÷ 7 = 1061.28... No. • Divisible by 11? Alternating digit sum = 7−4+2−9 = −4; not divisible by 11. No. • Divisible by 13? 7429 ÷ 13 = 571.46... No. • Divisible by 17? 7429 ÷ 17 = 437. Yes! ✓
Since 17 divides 7429 evenly, 7429 is NOT prime — it is composite.
Step 1: Divide 7429 by 17 7429 ÷ 17 = 437 Verification: 17 × 437 = 7429 ✓
Step 2: Factorise 437 Is 437 prime? Check divisibility up to √437 ≈ 20.9 • Divisible by 2? No (odd). • Divisible by 3? 4+3+7 = 14; not divisible by 3. No. • Divisible by 5? No. • Divisible by 7? 437 ÷ 7 = 62.4... No. • Divisible by 11? Alternating sum = 4−3+7 = 8; not divisible by 11. No. • Divisible by 13? 437 ÷ 13 = 33.6... No. • Divisible by 17? 437 ÷ 17 = 25.7... No. • Divisible by 19? 437 ÷ 19 = 23. Yes! ✓
Step 3: Factorise 23 23 is a prime number (divisible only by 1 and 23).
Result: 7429 = 17 × 19 × 23
Visual factor tree:
7429
/ \
17 437
/ \
19 23
Reading the leaves (bottom nodes): 17, 19, 23 — all prime.
Prime factorization: 7429 = 17 × 19 × 23
In exponent notation: 7429 = 17¹ × 19¹ × 23¹ (Each prime factor appears exactly once — all exponents are 1.)
Confirming that 17 × 19 × 23 = 7429:
Step 1: 17 × 19 17 × 19 = 17 × (20 − 1) = 340 − 17 = 323
Step 2: 323 × 23 323 × 23 = 323 × (20 + 3) = 323 × 20 + 323 × 3 = 6,460 + 969 = 7,429 ✓
So 17 × 19 × 23 = 7,429 ✓
Note on the primes: • 17 is the 7th prime number. • 19 is the 8th prime number. • 23 is the 9th prime number. 7429 is the product of three consecutive primes (17, 19, 23)!
All factors (divisors) of 7429:
Since 7429 = 17 × 19 × 23, the factors are all possible products of subsets of {17, 19, 23}:
Factor | Value 1 | 1 17 | 17 19 | 19 23 | 23 17 × 19 | 323 17 × 23 | 391 19 × 23 | 437 17 × 19 × 23 | 7429
Total number of factors: 2³ = 8 (since all prime exponents are 1, and (1+1)(1+1)(1+1) = 8)
Sum of factors: 1 + 17 + 19 + 23 + 323 + 391 + 437 + 7429 = 8,640
7429 = 17 × 19 × 23. Divide 7429 by 17 to get 437, then divide 437 by 19 to get 23. Since 23 is prime, the factorization is complete: 7429 = 17 × 19 × 23.
No, 7429 is not a prime number. It is composite because it can be divided evenly by 17: 7429 ÷ 17 = 437. Its prime factors are 17, 19, and 23.
7429 has 8 factors: 1, 17, 19, 23, 323, 391, 437, and 7429. These come from all combinations of its prime factors 17, 19, and 23.
First: 17 × 19 = 323. Then: 323 × 23 = 323 × 20 + 323 × 3 = 6,460 + 969 = 7,429. So 17 × 19 × 23 = 7,429 ✓
How Many Cubes of Edge 4 cm — Volume Division Problems
To find how many 4 cm cubes fit in a larger cube or cuboid, divide total volume by volume of small cube (64 cm³). Example: 12 cm cube gives 27 small cubes.
How Many Hundreds Make a Lakh?
1000 hundreds make a lakh. 1 lakh = 1,00,000 = 100 × 1000 hundreds. Learn the Indian number system with place values and conversion table.
How Many Lakhs Make 1 Crore?
Learn exactly how many Lakhs are in 1 Crore. Understand the Indian numbering system, the placement of zeros, and how to convert Lakhs into Crores effortlessly.
How Many Lakhs Make One Crore?
Learn exactly how many Lakhs make One Crore in the Indian Number System. Understand the zeroes and simple conversion maths for 1 Crore.
How Many Multiples of 4 Lie Between 10 and 250?
Learn how to solve the classic Class 10 Arithmetic Progression (AP) math problem: How many multiples of 4 lie between 10 and 250. Step-by-step solution.
Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.