What are the total number of divisors of 600(including 1 and 600)?
If N=ap $\times$ bq $\times$ cr.... then the number of factors of N = (p+1)(q+1)(r+1) ....
600 = 23 $\times$ 3 $\times$ 52
So number of factors of 600 = (3+1)(1+1)(2+1) = 24
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What is the sum of the squares of the first 20 natural numbers (1 to 20)? |
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In the polynomial f(x) = $x^5 + a\times x^3 + b\times x^4 +c\times x + d$, all coefficients a, b, c, d are integers. If 3 + $\sqrt{7}$ is a root, which of the following must be also a root?(Note that x^n denotes the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the square root of u, or the number which when multiplied by itself, gives the number u)? |
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How many divisors (including 1, but excluding 1000) are there for the number 1000? |
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