Question
How many divisors does the number 5040
have?Solution
First, find the prime factorization of 5040: 5040 ÷ 2 = 2520 2520 ÷ 2 = 1260 1260 ÷ 2 = 630 630 ÷ 2 = 315 315 ÷ 3 = 105 105 ÷ 3 = 35 35 ÷ 5 = 7 So, the prime factorization of 5040 is: 5040 = 2⁴ × 3² × 5 × 7. The formula for the number of divisors is: (Number of divisors) = (Exponent of 2 + 1)(Exponent of 3 + 1)(Exponent of 5 + 1)(Exponent of 7 + 1). Therefore, the number of divisors = (4 + 1)(2 + 1)(1 + 1)(1 + 1) = 5 × 3 × 2 × 2 = 60. Correct option: e
3, 10, 29, 66, ?
In each of the following series, one term is missing. Find the missing term.
7, 11, 19, 35, 67, ?
What will come in place of the question mark (?) in the following series?
72, 78, 90, ?, 132, 162
What will come in place of the question mark (?) in the following series?
12, 13, 22, 47, 96, 177, ?
8 12 39 ? 180 216
...What value should come in the place of (?) in the following number series?
14, 18, ?, 43, 68, 104
21 24 22 25 23 ?
...What value should come in the place of (?) in the following number series?
300, 421, 252, ?, 188, 549
What will come in place of the question mark (?) in the following series?
35, 38, 46, ?, 85, 120
What will come in place of the question mark (?) in the following series?
17, 81, 131, 169, 197, ?
