How many positive factors does 840 have ?
32
If \(N = p^{a} \times q^{b} \times r^{c} \times \ldots\), the number of positive factors is \((a + 1)(b + 1)(c + 1)\ldots\).
Prime factorisation: \(840 = 2^{3} \times 3^{1} \times 5^{1} \times 7^{1}\).
Number of factors \(= (3 + 1)(1 + 1)(1 + 1)(1 + 1) = 4 \times 2 \times 2 \times 2 = 32\).
Check: \(8 \times 3 \times 5 \times 7 = 840\).
Hence, 32.
Important Questions from Multiples and Factors
Let p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself. If q > p and both are two-digit numbers, and r > s and both are one-digit numbers, then the value of the expression \(\frac{p-q-1}{r-s}\) is:
Find the greatest three-digit number which is a multiple of 8.
The sum of three consecutive multiples of 7 is 840. The smallest of these multiples is:
If 2160 = 2 a × 3 b × 5 c , then the value of 3 a × 2 -b × 5 -c will be –
Find the number of ways in which 8064 can be resolved as the product of two factors ?
