Nooo Find the smallest possible p such that 26010p is a square number help plz

Question

ScanSolve AI Tutor · Accepted Answer

Let's solve this step by step. Step 1: Factor 26010 into its prime factors. 26010 = 2 × 3 × 5 × 7 × 13 Step 2: For a number to be a perfect square, all prime factors must have even exponents. Currently, the exponents of the prime factors are: 2: 1 (odd) 3: 1 (odd) 5: 1 (odd) 7: 1 (odd) 13: 1 (odd) Step 3: To make each exponent even, we need to multiply by each prime factor that has an odd exponent. Therefore, we need to multiply by: p = 2 × 3 × 5 × 7 × 13 Step 4: Calculate p. p = 2 × 3 × 5 × 7 × 13 = 2730 Step 5: The smallest possible p such that 26010p is a square number is 2730.

Nooo Find the smallest possible p such that 26010p is a square number help plz

Step-by-step solution

Factor 26010 into its prime factors.

For a number to be a perfect square, all prime factors must have even exponents.

To make each exponent even, we need to multiply by each prime factor that has an odd exponent.

Calculate p.

The smallest possible p such that 26010p is a square number is 2730.

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