# The sum of 6 consecutive integers is 153. What is their product?

Relevance
• x  + (x  + 1) + (x. + 2) + (x  + 3) + (x  + 4)  + (x  + 5) = 153

6x  + 15    = 153

6x   = 138

x   = 23

Product   =  23 x 24 x 25 x 26 x 27 x 28

Product   =  22 604 400

• Login to reply the answers
• Let x = start number.

Equation:

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 153

6x + 15 = 153

6x = 138

x = 23

Their product:

= 23 * 24 * 25 * 26 * 27 * 28

= 271,252,800

• Login to reply the answers
• Let the 6 numbers be

x-2, x-1, x , x+1, x+2, x+3.

their sum is

6x+3=153=>x=25

Thus their product=

23*24*25*26*27*28=

271252800.

• Login to reply the answers
• Put the integers = (n-2), (n-1), n, (n+1). (n+2), (n+3). Sum = 6n+3 = 153, n = 25.

Product = n(n+3)(n^2-1)(n^2-4) = 25*28*624*621 = 700*387,504 = 271,252,800.

• Login to reply the answers
• 153 = m - 2.5 + m - 1.5 + m - 0.5 + m + 0.5 + m + 1.5 + m + 2.5

153 = 6m

25.5 = m

(m - 2.5) * (m - 1.5) * (m - 0.5) * (m + 0.5) * (m + 1.5) * (m + 2.5) =>

(m^2 - 6.25) * (m^2 - 2.25) * (m^2 - 0.25) =>

(1/4) * (4m^2 - 25) * (1/4) * (4m^2 - 9) * (1/4) * (4m^2 - 1) =>

(1/64) * (4m^2 - 25) * (4m^2 - 9) * (4m^2 - 1) =>

(1/64) * (4 * (51/2)^2 - 25) * (4 * (51/2)^2 - 9) * (4 * (51/2)^2 - 1) =>

(1/64) * (4 * 2601/4 - 25) * (4 * 2601/4 - 9) * (4 * 2601/4 - 1) =>

(1/64) * (2601 - 25) * (2601 - 9) * (2601 - 1) =>

(1/64) * 2576 * 2592 * 2600 =>

(1/64) * 26 * 100 * (2584 - 8) * (2584 + 8) =>

(1/32) * 13 * 100 * 4 * (646 - 2) * 4 * (646 + 2) =>

(1/2) * 13 * 100 * 4 * (323 - 1) * (323 + 1) =>

2 * 13 * 100 * (323 - 1) * (323 + 1) =>

26 * (323^2 - 1) * 100 =>

26 * ((300 + 23)^2 - 1) * 100 =>

26 * (90000 + 6900 + 6900 + 529 - 1) * 100 =>

26 * (90000 + 13800 + 528) * 100 =>

26 * (103800 + 528) * 100 =>

26 * 104328 * 100 =>

(25 + 1) * 104328 * 100 =>

(25 + 1) * 4 * 26082 * 100 =>

100 * 100 * 26082 + 4 * 100 * 26082 =>

260,820,000 + 10,432,800 =>

270,000,000 + 1,252,800 =>

271,252,800

• Login to reply the answers
• Here is the algebraic way of solving the problem. Method works every time.

Your consecutive integers are: a, a + 1, a + 2, a+ 3, a +4, a+5 = 153

6a + 15 = 153

6a = 153 - 15

6a = 138

a = 23

Your integers are 23, 24, 25 , 26, 27, 28

Check

23 + 24 +25 +26 +27 + 28 = 153

• Login to reply the answers
• The sum of the numbers is 153.

There are 6 of them.

So the average is 153/6 = 25.5

If you think about it, the average would be right between the middle two integers, so they must be 25 and 26. And from there we can figure out all 6.

23, 24, 25, 26, 27, 28

Now find their product by multiplying them together:

23 * 24 * 25 * 26 * 27 * 28

= 271,252,800

UPDATE:

If you wanted to be a little more formal, you could use algebra.

Let the first integer be n.

Let the next integer be n+1.

etc.

The sum is 153:

n + n+1 + n+2 + n+3 + n+4 + n+5 = 153

6n + 15 = 153

6n = 138

n = 138/6

n = 23

So the first number is 23 and then the others are 24, 25, etc. Like before, multiply them together to get the product.

• Login to reply the answers
• x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) = 153

6x + 15 = 153

6x = 138

x = 23.  So the consecutive integers are 23, 24, 25, 26, 27, and 28.

23 * 24 * 25 * 26 * 27 * 28 = 271,252,800.  Final.  (Very tedious without the use of a calculator, but it's obtainable.)

• Login to reply the answers
• Puzzling
• Login to reply the answers
• Login to reply the answers