The sum of 25 adjacent even numbers must be a multiple of 25

Let the first even bit n, then the last even bit n+2*(25-1).

The first number is n (is even); The last number is n+48 ==> and the combination is: 2*(n+24).

The second number is n+2*(2-1)=n+2; The penultimate number is n+46 ==> and the combination is: 2*(n+24).

The third number is n+2*(3-1)=n+4; The penultimate number is n+44 ==> and the sum is: 2*(n+24).

The twelfth number is n+2*(12-1)=n+22; The twelfth digit from the bottom is n+26 ==> and the sum is: 2*(n+24).

The thirteenth number is n+2*(13-1)=n+24 ==> the number in the middle.

Apparently there are twelve 2*(n+24) and one n+24 that add up: 25*(n+24).

It means that as long as it is an adjacent 25 even numbers, it must be (n+24) times of 25.

From this, it can be seen that the number of 25 adjacent is a multiple of 25, and it has nothing to do with the number itself, only adjacent!! can prove

Let the first even number be x, then.

Second: x+2

The third: x+4

25th: x+48

Then the sum of these 25 numbers is: x+(x+2)+. x+4) = 25x+600 Because 600 is a multiple of 25, 25x is definitely a multiple of 25, so (25x+600) is also definitely a multiple of 25. Certification.

A number is both a factor of 25 and a multiple of 25, and this number is 25;

So the answer is: 25

Their greatest common factor is (2) and the least common multiple is (60).

These two numbers are 10 and 12

4 5 = 20, it can only be said that 4 and 5 are both factors of 20, and 20 is a multiple of 4 and 5; It cannot be said that 4 and 5 are both factors, and 20 is a multiple

Therefore, it is judged to be false

4 5 = 20, it can only be said that 4 and 5 are both factors of 20, and 20 is a multiple of 4 and 5; It cannot be said that 4 and 5 are both factors, and 20 is a multiple

Therefore, it is judged to be false

260 5=52 That's the middle number.

They are 48 50 52 54 56

The sum of two adjacent even numbers is 22, their greatest common factor is (2), and the least common multiple is (60).

Their greatest common factor is (2) and the least common multiple is (60).

These two numbers are 10 and 12

2 (greatest common factor) 60 (smallest common multiple).

Two adjacent even numbers, the smaller number is 2 less than the larger number, corresponding to 25%, so.

The greater number is 2 25% = 8

The smaller number is 8-2=6

Let the larger one be x, and the smaller one is (

x-(x = these two numbers are 6,8.)

A number that is a multiple of 2 or 5 at the same time must be even. That's right.

Analysis: Their greatest common factor is 10, so to be a multiple of 10, the number must be an even number like .

Definitely, it can only be an integer like that.