Explanation: how many divisors of 360? What is the sum of these divisors?

360 = 2 × 2 × 2 × 3 × 3 × 5 = 23 × 32 × 5, so 360 has (3 + 1) × (2 + 1) × (1 + 1) = 24 divisors; the sum of divisors is (1 + 2 + 22 + 23) × (1 + 3 + 32) × (1 + 5) = 1170; answer: there are 24 divisors of 360, and the sum of these divisors is 1170

There is a natural number, it has 4 different prime factors, 32 divisors, there is a prime factor is two digits, the sum of its numbers is 11, the prime number is required
1. There is a natural number, which has four different prime factors and 32 divisors. There is a prime factor which is two digits, and the sum of its numbers is 11. The prime number should be as large as possible. What is the minimum of the natural number?
2. It is known that the sum of two natural numbers is 60, and the sum of their greatest common divisor and least common multiple is 84?

1. According to the meaning of the question, the prime factor of two digits should be 83. To minimize this number, the other three prime factors should be 2, 3 and 5. Then the minimum natural number is 2 * 2 * 2 * 3 * 5 * 83 = 99602. If the greatest common divisor of these two numbers is x, then these two numbers are ax and BX respectively. The least common multiple is ABX

1. 3 and 9 are all 9 ()
A. Prime factor B. prime number C. factor

1. 3 and 9 are all factors of 9

In Cartesian coordinate system, given points a (4,0), B (0,3), if a right triangle is congruent with RT △ ABO, and they have a common edge, please write out the unknown vertex coordinates of the triangle (do not need to write the calculation process). (hint: consider the three cases of Ao, Bo, AB being the common edge respectively)

As shown in the figure, if AB is the common edge, there are three answers (72259625), (4,3), (2825, - 2125); if Bo is the common edge, there are two answers (- 4,3) and (- 4,0); if Ao is the common edge, there are two answers (0, - 3) and (4, - 3)

Solution equation (x-2.5) divided by (1-40%) = 10 / 9

（x-2.5）÷3/5=10/9
x-2.5=10/9*3/5
x-5/2=2/3
x=5/2+2/3
x=19/6

Let vector group A1, A2, A3 be linearly independent in linear algebra, and prove that vector group B1 = a1 + a2-2a3, B2 = a1-a2-a3
Let vector group A1, A2, A3 be linearly independent in linear algebra, and prove that vector group B1 = a1 + a2-2a3, B2 = a1-a2-a3, B3 = a1 + a3 are linearly independent

Prove by definition
Let k1b1 + k2b2 + k3b3 = 0
K1 (a1 + a2-2a3) + K2 (a1-a2-a3) + K3 (a1 + a3) = 0
(k1+k2+k3)a1+(k1-k2)a2+(k1-k2+k3)a3=0
Because A1, A2, A3 are linearly independent, there must be
k1+k2+k3=0
k1-k2=0
k1-k2+k3=0
So the solution is K1 = K2 = K3 = 0
From the definition of linear independence, we know that b1.b2.b3 is linear independence

The approximate solution of the equation X3 + 1.1x2 + 0.9x-1.4 = 0 is obtained by dichotomy, so that the error does not exceed 0.01
Such as the title

The dichotomy is based on the fact that the continuous function y = f (x) satisfies f (a) f (b) at two points a and B

Let Sn be the sum of the first n terms of the arithmetic sequence {an}, if a5a3 = 59, then s9s5 = ()
A. 1B. -1C. 2D. 12

Let the first term of the arithmetic sequence {an} be A1. From the properties of the arithmetic sequence, we can get a1 + A9 = 2a5, a1 + A5 = 2A3, ｜ s9s5 = a1 + a92 × 9a1 + a52 × 5 = 9a55, A3 = 95 × 59 = 1, so we choose a

Let f (x) = loga (x) (a > 0 and a is not equal to 1) if f (x1.x2.x2009) = 8, then f (x1 ^ 2) +. F (X2009 ^ 2) is equal to several
Wait for 16

f（x1.x2.x2009)=log a(x1.x2.x2009)=log a x1+log a x2+…… +log a(x2009)=8
f(x1^2)+.f(x2009^2)=log a(x1^2)+…… +log a(x2009^2)=2[log a(x1)+…… +log a(x2009)]
=2×8=16

As shown in the figure, take sides AC and BC of △ ABC as one side respectively, and make square ACDE and cbfg outside △ ABC. Point P is the midpoint of EF. Prove that the distance from point P to AB is half of ab

Then Er ∥ PQ ∥ FS, ∵ P is the midpoint of EF, ∥ q is the midpoint of RS, ∥ PQ is the median line of trapezoidal EFSR, ∥ PQ = 12 (ER + FS), ∥ AE = AC (equal side length of square), ∥ aer = ∥ cat (equal residual angle of the same angle), ∥ r = ∥ ATC = 90 °, ∥ RT △ aer ≌ RT △ cat (AAS), the same as RT △ BFS ≌ RT △ CB T，∴ER=AT，FS=BT，∴ER+FS=AT+BT=AB，∴PQ=12AB．

Explanation: how many divisors of 360? What is the sum of these divisors?