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2026-01-01
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2026-02-28
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<p>Prime numbers are a set of natural numbers that can only be divided by 1 and the number itself. Here are two important ways to determine whether a number is prime or not.</p>
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<p>Prime numbers are a set of natural numbers that can only be divided by 1 and the number itself. Here are two important ways to determine whether a number is prime or not.</p>
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<h3>By Divisibility Method:</h3>
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<h3>By Divisibility Method:</h3>
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<p>To find whether a number is prime or not, we use the divisibility method to check. If a number is divisible by 2, 3, 5, or other small primes, then it is not a prime number. Prime numbers are only divisible by 1 and themselves, so if a number is divisible by the number itself and 1, it is a prime number.</p>
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<p>To find whether a number is prime or not, we use the divisibility method to check. If a number is divisible by 2, 3, 5, or other small primes, then it is not a prime number. Prime numbers are only divisible by 1 and themselves, so if a number is divisible by the number itself and 1, it is a prime number.</p>
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<p>For example: To check whether 137 is a prime number,</p>
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<p>For example: To check whether 137 is a prime number,</p>
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<p><strong>Step 1:</strong>137 ÷ 2 = 68.5 (<a>remainder</a>≠ 0)</p>
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<p><strong>Step 1:</strong>137 ÷ 2 = 68.5 (<a>remainder</a>≠ 0)</p>
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<p><strong>Step 2:</strong>137 ÷ 3 ≈ 45.67 (remainder ≠ 0)</p>
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<p><strong>Step 2:</strong>137 ÷ 3 ≈ 45.67 (remainder ≠ 0)</p>
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<p><strong>Step 3:</strong>137 ÷ 5 = 27.4 (remainder ≠ 0)</p>
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<p><strong>Step 3:</strong>137 ÷ 5 = 27.4 (remainder ≠ 0)</p>
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<p>Since no divisors are found, 137 is a prime number.</p>
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<p>Since no divisors are found, 137 is a prime number.</p>
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<h3>By Prime Factorization Method:</h3>
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<h3>By Prime Factorization Method:</h3>
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<p>The<a>prime factorization</a>method involves breaking down a<a>composite number</a>into the<a>product</a>of its prime factors. The method of prime factorization helps identify the prime numbers up to 1000 by building the smallest blocks of any given number.</p>
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<p>The<a>prime factorization</a>method involves breaking down a<a>composite number</a>into the<a>product</a>of its prime factors. The method of prime factorization helps identify the prime numbers up to 1000 by building the smallest blocks of any given number.</p>
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<p>For example: The prime factorization of 1000: Break it down into the smallest prime numbers until it can’t divide anymore.</p>
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<p>For example: The prime factorization of 1000: Break it down into the smallest prime numbers until it can’t divide anymore.</p>
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<p><strong>Step 1:</strong>1000 ÷ 2 = 500</p>
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<p><strong>Step 1:</strong>1000 ÷ 2 = 500</p>
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<p><strong>Step 2:</strong>Now, divide 500, 500 ÷ 2 = 250</p>
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<p><strong>Step 2:</strong>Now, divide 500, 500 ÷ 2 = 250</p>
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<p><strong>Step 3:</strong>Now take 250, 250 ÷ 2 = 125</p>
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<p><strong>Step 3:</strong>Now take 250, 250 ÷ 2 = 125</p>
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<p><strong>Step 4:</strong>Take 125, since 125 ends in 5, divide the number by 5 ,125 ÷ 5 = 25</p>
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<p><strong>Step 4:</strong>Take 125, since 125 ends in 5, divide the number by 5 ,125 ÷ 5 = 25</p>
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<p><strong>Step 5:</strong>Take 25, 25 ÷ 5 = 5</p>
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<p><strong>Step 5:</strong>Take 25, 25 ÷ 5 = 5</p>
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<p><strong>Step 6:</strong>At last, take 5. 5 ÷ 5 = 1 (since 5 is a prime number, and dividing by 5 gives 1)</p>
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<p><strong>Step 6:</strong>At last, take 5. 5 ÷ 5 = 1 (since 5 is a prime number, and dividing by 5 gives 1)</p>
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<p>Therefore, the prime factorization of 1000 is: 1000 = 23 × 53.</p>
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<p>Therefore, the prime factorization of 1000 is: 1000 = 23 × 53.</p>
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