MATH SOLVE

3 months ago

Q:
# How many positive integers less than 2018 are divisible by at least 3, 11, or 61?

Accepted Solution

A:

To find all the positive integers less than 2018 that are divisible by 3, 11, and 61, you will use what you know about factors.

3, 11, and 61 are all answers. So are 33, 183, 671, and 2013.

If you put these in factors, the product will be divisible by them!

3 x 11 = 33

3 x 61 = 183

11 x 61 = 671

3 x 11 x 61 = 2013

Take each number and square it, cube it, etc...

9, 27, 81, 243, 729

121, 1331

9 x 11 = 99

27 x 11 = 297

81 x 11 = 891

121 x 9 =1089

121 x 3 = 363

61 x 9 = 549

61 x 27 = 1647

Everything in bold is a correct answer.

3, 11, and 61 are all answers. So are 33, 183, 671, and 2013.

If you put these in factors, the product will be divisible by them!

3 x 11 = 33

3 x 61 = 183

11 x 61 = 671

3 x 11 x 61 = 2013

Take each number and square it, cube it, etc...

9, 27, 81, 243, 729

121, 1331

9 x 11 = 99

27 x 11 = 297

81 x 11 = 891

121 x 9 =1089

121 x 3 = 363

61 x 9 = 549

61 x 27 = 1647

Everything in bold is a correct answer.