The number n^2 is greater than 1,400,000 and has four different prime factors. If n is a positive odd integer, what is the least possible value of n?
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n is odd and have 4 different prime factors.
So even prime factor is not possible.
The smallest 4 prime odd prime numbers are 3,5,7 and 11.
approach-1:
√1400000 = 1183.33
so we need a number greater than or 1184
3×5×7×11 = 1155 <1184
3×5×7×11×3 = 1155×3 = 3465 > 1184
So number smallest number is 3465
approach-2:
The smallest number with 3,5,7 and 11 as prime factors = 3×5×7×11 = 1155
1155² = 1334025 < 1400000
so the next smallest number is = (3×5×7×11)×3 = 1155×3 = 3465
3465² > 1400000
So even prime factor is not possible.
The smallest 4 prime odd prime numbers are 3,5,7 and 11.
approach-1:
√1400000 = 1183.33
so we need a number greater than or 1184
3×5×7×11 = 1155 <1184
3×5×7×11×3 = 1155×3 = 3465 > 1184
So number smallest number is 3465
approach-2:
The smallest number with 3,5,7 and 11 as prime factors = 3×5×7×11 = 1155
1155² = 1334025 < 1400000
so the next smallest number is = (3×5×7×11)×3 = 1155×3 = 3465
3465² > 1400000
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