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Question

Difficulty: EasyPrime Numbers and Prime Factorization

What is the smallest prime factor of 143143?

Answer: 11

Answer

The smallest prime factor of 143 is 11.
To find the smallest prime factor of 143, test prime numbers in increasing order starting from 2. Testing 2, 3, 5, and 7 shows none are factors of 143. Testing 11 yields 143÷11=13143 \div 11 = 13, which is an integer. Thus, 143=11×13143 = 11 \times 13. Since 11 and 13 are both prime, 11 is the smallest prime factor of 143.

Step-by-Step Solution

1
Test divisibility of 143 by small prime numbers in ascending order
143 is not divisible by 2, 3, 5, or 7.
Basic divisibility rules eliminate 2 (odd), 3 (digit sum 8), and 5 (ends in 3). Direct division shows 143 = 7 × 20 + 3.
2
Test divisibility by the next prime number, 11
143 divided by 11 equals 13 exactly.
Since 143 = 11 × 13 and 11 is prime, 11 is a prime factor.
3
Identify the smallest prime factor
The prime factors of 143 are 11 and 13, making 11 the smallest.
No prime number smaller than 11 divides 143.

Key Concept

Prime Factorization
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Topics

Prime Numbers and Prime Factorization

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