Split 14 into the sum of several natural numbers, and then find the product of these numbers

Splitting method with the largest product:

If 2: 14 = 7 + 7, 7 * 7 = 49

If 3: 14=5+5+4, 5*5*4 = 100, if 4: 14=4+4+3+3, 4*4*3*3 = 144 If 5:

14 = 3 + 3 + 3 + 2, 3 * 3 * 3 * 3 * 2 = 162 if 6: 14 = 3 + 3 + 2 + 2 + 2 + 2, 3 * 3 * 2 * 2 * 2 * 2 = 144

The largest is split into 5, and the product is 3*3*3*3*2=162

With the knowledge of advanced mathematics, I know that it is best to press e to split, and now it is required to split into whole numbers, so try to split into 3.

If the original number is a multiple of 3, that's fine;

If the original number is divided by 3 and the remainder is 1, then 2 2's (or 1 4') are split first, and the rest are split into 3;

If the original number is divided by 3 and the remainder is 2, then 1 2 is split, and the rest is split into 3.

1. It is impossible to detach the number of 5 and above, otherwise there must be 2 (n-2) >n;

2. It is impossible to remove 1, otherwise 1 n

3. If you take out 4, you can split it into 2 2s;

4. If there are 3 2s, you can split them into 2 3s, because 23=82.

The conclusion is: all split into 3 and 2, with a maximum of 2 2s.

The specific method is to divide the situation according to the remainder of the number n divided by 3 as mentioned above.

Split into two numbers, the product is up to 7 7 = 49

Split into three numbers, the product is up to 4 5 5 = 100

Split into four numbers, the product is up to 3 3 4 4 = 144 split into five numbers, the product is up to 2 3 3 3 3 = 162 beats into six numbers, the product is up to 2 2 2 2 3 3 = 144 split into seven numbers, the product is up to 2 2 2 2 2 2 2 = 128 So, the maximum product is 162.

Except for 1, the more times you dismantle, the greater the product.

That is, how many 2s are split into

The multiplication of seven 2s is the 7th power of 2.

Split 14 into the sum of several natural numbers, and maximize the product of these natural numbers. What is the maximum product?

If 14 = 2 + 2 + 2 + 2 + 2 + 2 + 2 then 2 2 2 2 2 2 = 128;

If 14 = 3 + 3 + 3 + 3 + 2, then 3 3 3 3 2 = 162;

If 14=4+4+4+2, then 4 4 4 2=128;

If 14 = 5 + 5 + 2 + 2, then 5 5 2 2 = 100;

If 14=6+6+2, then 6 6 2=72;

If broken down into unequal natural numbers, their product is smaller.

So when. 14 = 3 + 3 + 3 + 3 + 2, then 3 3 3 3 2 = 162;Utmost!

The product of the most split 3 is the largest.

The maximum product is 3x3x3x3x2=162

14 = 3 + 3 + 3 + 2, 3 3 3 3 2 = 162, so if 14 is divided into the sum of several natural numbers, and then the product of these numbers is calculated, the largest number in the product is 162

So the answer is: 162

Problem solving idea: Split a natural number n into the sum of several natural numbers, only when these split numbers are composed of 2 or 3, where 2 is at most 2, the product of these split numbers is the largest So 14 can be divided into 3+3+3+3+2, and then calculate the product

14 = 3 + 3 + 3 + 2, 3 3 3 3 2 = 162, so if 14 is divided into the sum of several natural numbers, and then the product of these numbers is calculated, the largest number in the product is 162

So the answer is: 162 ,7,3 3 3 5 is the maximum,2,daan3 3 3 5,2,3 3 3 3 2 maximum,0,split 14 into 7 2s, the product is 128,0,

In order to maximize the product of the natural dust bends after the splitting, the number of partitions should be close to the median of this number. So sell envy.

So the maximum product is 3 4 3 4 144

Split 13 into the sum of several natural numbers: to make the product of some natural numbers in this early book the maximum, to Lu Yi less can not be split into 1, because, 1 times any number is still any number, therefore, 1 is split into 2 + 2 + 3 + 3 + 3 13, the product of these natural numbers is: 2x2x3x3x3 108, 2 split into 2 + 3 + 4 + 4 13, the product is:

2x3x4x4 96,3 is divided into 2+3+3+5 13, the product is: 2x3x3x5 90, from the above 3 split number groups, the larger the split numbers, the smaller their product is, so, only 1 The product of the split number group is the largest.

14 is to split into 5 natures.

The sum of numbers: 3+3+3+3+2, the maximum product of these 5 natural numbers is 162.

Specific analysis process:

If we split 14 into the sum of 2 natural numbers: 14 = 7 + 7, the product of these 2 natural numbers is the largest: 7*7 = 49;

If we split 14 into the sum of 3 natural numbers: 14 = 5 + 5 + 4, the product of these 3 natural numbers is the maximum: 5 * 5 * 4 = 100;

If you split 14 into the sum of 4 natural numbers: 14 = 4 + 4 + 3 + 3, the product of these 3 natural numbers is the maximum: 4 * 4 * 3 * 3 = 144 If you split 14 into the sum of 5 natural numbers:

14 = 3 + 3 + 3 + 3 + 2, the product of these 3 natural numbers is the maximum: 3*3*3*3*2 = 162;

If 14 is split into the sum of 6 natural numbers: 14 = 3 + 3 + 2 + 2 + 2 + 2, the product of these 6 natural numbers is the maximum: 3 * 3 * 2 * 2 * 2 * 2 = 144 so 14 is split into the sum of 5 natural numbers:

3+3+3+3+2, the maximum product of these 5 natural numbers is 162.

The maximum product is: copy162.

14 = 3 + 3 + 3 + 3 + 2, 3 3 3 3 2 = 162, so if bai divides 14 into the sum of several natural numbers, then calculates these.

The product of the zhi number is the largest dao in the product

The number is 162.

If the integer b is divided by the non-zero integer a, the quotient is an integer, and the remainder is zero, then we say that b is divisible by a (or that a is divisible by b), b is the dividend, and a is the divisor, i.e., a|b（“|is an divisibility symbol) and is pronounced as "a divisible by b" or "b divisible by a". A is called the divisor (or factor) of b, and b is called a multiple of a. Divisibility is a special case of exhaustion.

Natural numbers are not equal: the product is the largest when 14 = 2 + 3 + 4 + 5, and the natural number can be equal if it is 120: the product is the largest when it is 14 = 3 + 3 + 3 + 3 + 2 and is 162

What is the maximum product of splitting 14 into the sum of several natural numbers and making the product of these natural numbers the largest?

The maximum product is: 162,

14 = 3 + 3 + 3 + 2, 3 3 3 3 2 = 162, so if 14 is divided into the sum of several natural numbers, and then the product of these numbers is calculated, the largest number in the product is 162

A: This product is 162