Study Guides/Maths/Prime Factorization of 7429
Study Guide · Maths

Prime Factorization of 7429 — 17 × 19 × 23

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.

Question (Click to Flip)

What is the prime factorization of 7429?

Answer

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.

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Key Facts

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.

Is 7429 a Prime Number?

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-by-Step Prime Factorization of 7429

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

Factor Tree of 7429

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.)

Verification — Multiply Back

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)!

Factors and Divisors of 7429

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

Questions and Answers

What is the prime factorization of 7429?+

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.

Is 7429 a prime number?+

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.

What are all the factors of 7429?+

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.

How do you verify that 17 × 19 × 23 = 7429?+

First: 17 × 19 = 323. Then: 323 × 23 = 323 × 20 + 323 × 3 = 6,460 + 969 = 7,429. So 17 × 19 × 23 = 7,429 ✓

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