# Math

This problem from China is almost 2000 years old: Find a number that when divided by 3 gives a remainder of 2, when divided by 5 gives a remainder of 3, and when divided by 7 gives a remainder of 4.

1. 👍 0
2. 👎 0
3. 👁 388
1. look up "Chinese Remainder Theorem"
and you will find many pages for this kind of problem

You will have to know how to do arithmetic in "modular arithmetic" , and this forum is not suitable to teach you that.
I just worked out the above problem using that method and got

263

If you have enough patience, here is another way to do that question which is very easy to understand:

divided by 3 gives a remainder of 1 :
4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 ..... 263

when divided by 5 gives a remainder of 4 :
4 9 14 19 24 29 34 39 43 49 53 59 ..... 263

when divided by 7 gives a remainder of 2 :
2 9 16 23 30 37 44 51 58 ...... 263

1. 👍 0
2. 👎 0
2. ignore the 2nd part of my answer to the above, the numbers don't even match. I cut and pasted from a previous solution but the numbers were not even the same

Also note that even though 263 is a solution, it is one of an infinite number. But it said to find "a number", so the answer of 263 is a correct answer.
If you want others, especially the smallest such number, proceed as follows
looking the the divisiors of 3, 5, and 7, we would have a LCM of 105
so 263 - 105 = 158 is another solution
158 - 105 = 53 is another, and the smallest.

the long and tedious way would be"

divided by 3 gives a remainder of 2 :
2 5 8 11 14 17 20 23 26 29 32 35 38 41 44 47 50 53 56 ..... 263

when divided by 5 gives a remainder of 3 :
3 8 13 18 23 28 33 38 43 48 53 58 ..... 263

when divided by 7 gives a remainder of 4 :
4 11 18 25 32 39 46 53 60 ...... 263

notice that 53 is the first such number.

1. 👍 0
2. 👎 0
3. Thank you so much for the help!

1. 👍 0
2. 👎 0

## Similar Questions

18. In 2000, the circulation of a local newspaper was 3,250. In 2001, its circulation was 3,640. In 2002, the circulation was 4,100. a. Find the percent of increase in the newspaper’s circulation from 2000 to 2001 and from 2001

2. ### math

Division of rational numbers find each product 1. 1/3 * 7 A. 1/21 B. 2 1/7 C. 2 1/3 D. 3/7 I think it is B 2. -7/9 * 3/5 A. 18/35 B. 7/15 C. -18/35 D. -7/15 I think it is C 3. 1/3 divided by 5/6 A. 2/5 B. 5/2 C. 2/15 D. 5/18 I

3. ### Algebra-Problems

Please help with my word problems? Solve the problem. The rabbit population in a forest area grows at the rate of 6% monthly. If there are 260 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be

4. ### algebra

from 1990 to 2000, the number of thousand visits by people to hawaii volcanoes national park increased by about 43.1 thousand visits. per year. In 2000, there were about 1529.6 thousand visits to the park. write an equation that

1. ### Algebra

If p(x) is a polynomial and is divided by (x-k) and a remainder is obtained, then that remainder is p(k). If the quadratic p(x)=x^2-3x+5 gives the same remainder when divided by x+k as it does when divided by x-3k find the value

2. ### Algebra I

Use A = P(1+r)^t to find the interest rate. \$2000 grows to \$2420 in 2 years. I have no idea how to go about this problem! Your help is appreciated. Thank you!!

3. ### Algebra

a student's work to solve 2 6/7 divided by 2/7 is shown below. which of the following statements do you agree with? 2 6/7 divided by 2/7 = 19/7 divided by 2/7= 7/19 times 2/7= 7/19 times 2/7=2/19 cross out the 7 in the first one

4. ### Algebra 2

For the period 1990-2002, the number s (in thousands)lf cellular telephone subscribers in the United States can be modified by S=858t^2 + 1412t + 4982 where t is the number of years since 1990. In what year did the number of

1. ### ss

Which effect(s) did European expansion have on China? Select the two correct answers. A. China was divided into European colonies. B. Britain forced China to participate in the opium trade. C. European nations cut off China from

2. ### algebra 1

From 1990 to 2000, the number of thousand visits by people to Bryce Canyon National Park increased about 23.9 thousand visits per year. In 2000, there were 1102.4 thousand visits to the park. Write an equation that gives the

3. ### Estimation decimal quotient

Use compatible numbers to find the each quotient ,2.90 divided by 29,48 divided by 3.2, 0.18 divided by 0.33,152 divided by 5.12,41.9 divided by 19,33.90 divided by 10.2, 502 divided by 9.5, 180.8 divided by 6 , 48 divided by

4. ### Estimating decimal quotient

Use compatible to find the following quotient 180.8 divided by 6 182divided by 11 55divided by 10.7 117.8divided by 0.12 0.6 divided by 5 145 divided by 0.3 60 divided by 5.9 1.8 divided by 20