Prime factorization is the process of expressing a number as a product of its prime factors. To find the prime factorization of 35280, we divide the number repeatedly by the smallest prime numbers until we reach 1. The prime factorization of 35280 is 2⁴ × 3² × 5 × 7².
Prime factorization of 35280 = 2⁴ × 3² × 5 × 7².
Division steps: 35280 → 17640 → 8820 → 4410 → 2205 → 735 → 245 → 49 → 7 → 1.
35280 = 16 × 9 × 5 × 49.
Number of factors of 35280 = (4+1)(2+1)(1+1)(2+1) = 90.
35280 is not a perfect square (since 5 appears to power 1, which is odd).
√35280 = 84√5 ≈ 187.83.
Step-by-step division:
35280 ÷ 2 = 17640 17640 ÷ 2 = 8820 8820 ÷ 2 = 4410 4410 ÷ 2 = 2205 2205 ÷ 3 = 735 735 ÷ 3 = 245 245 ÷ 5 = 49 49 ÷ 7 = 7 7 ÷ 7 = 1
So: 35280 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 × 7 = 2⁴ × 3² × 5 × 7²
Let us verify: 2⁴ × 3² × 5 × 7² = 16 × 9 × 5 × 49 = 16 × 9 = 144 144 × 5 = 720 720 × 49 = 35,280 ✓
So the prime factorization is correct: 35280 = 2⁴ × 3² × 5 × 7²
Using the formula for number of factors: If n = p^a × q^b × r^c... Number of factors = (a+1)(b+1)(c+1)...
35280 = 2⁴ × 3² × 5¹ × 7² Number of factors = (4+1)(2+1)(1+1)(2+1) = 5 × 3 × 2 × 3 = 90
So 35280 has 90 factors.
35280 = 2⁴ × 3² × 5 × 7² = (2²)² × 3² × 5 × (7)² = (4 × 3 × 7)² × 5 = 84² × 5
√35280 = 84√5 ≈ 84 × 2.236 ≈ 187.83
Note: 35280 is not a perfect square because 5 appears to an odd power (5¹).
The prime factorization of 35280 is 2⁴ × 3² × 5 × 7² = 16 × 9 × 5 × 49. Step-by-step: 35280 ÷ 2 = 17640, ÷2 = 8820, ÷2 = 4410, ÷2 = 2205, ÷3 = 735, ÷3 = 245, ÷5 = 49, ÷7 = 7, ÷7 = 1.
35280 = 2⁴ × 3² × 5¹ × 7². Number of factors = (4+1)(2+1)(1+1)(2+1) = 5 × 3 × 2 × 3 = 90. So 35280 has 90 factors.
No. 35280 = 2⁴ × 3² × 5¹ × 7². Since 5 appears to the power 1 (odd), 35280 is not a perfect square. For a perfect square, all prime factors must appear to even powers.
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