# Divisibility by 7

May 7th, 2015
Studypool Tutor
Price: \$10 USD

Tutor description

Divisibility by 7: Now we will study divisibility by 7. One book on speed arithmetic says that these tests are just too complicated, and you should just divide by 7. I agree to some extent, but my calculator still will not let me enter really large numbers. One interesting way (found in some books) is to take the two left-most digits, multiply the left digit by 3 and add it to the second digit. Replace these two digits with

Word Count: 1499
Showing Page: 1/5
Divisibility by 7Divisibility by 7: Now we will study divisibility by 7. One book on speed arithmetic says that these tests are just too complicated, and you should just divide by 7. I agree to some extent, but my calculator still will not let me enter really large numbers. One interesting way (found in some books) is to take the two left-most digits, multiply the left digit by 3 and add it to the second digit. Replace these two digits with the result. Then we can keep repeating, always dealing with only the two left-most digits, until we end up with a small number which is either divisible by 7 or not. Pretend we have a two digit number, 10x+y. We multiply the left digit by 3 and add the second digit: 3x+y. All we did was just subtract 7x. If 3x+y is divisible by 7, then so is 10x+y. This works at the left end of a long number, too. The two left-most digits are 10x+y times some power of 10. Multiplying the left digit by 3 and adding the second digit gives us 3x+y times the same power of 10. And we subtracted off 7 times the same power of 10. Again, divisibility by 7 was not altered. 4712954379 1912954379 1212954379 512954379 162954379 92954379 29954379 15954379 8954379 3354379 1254379 554379 204379 64379 22379 8379 2779 1379 679 259 119 4949 is divisible by 7. We could have stopped the process once we got a number that was small enough for my calculator, and divided the current number by 7. Since 49 is divisible by 7, every number above it is also divisible by 7. Modu

## Review from student

Studypool Student
" Top quality work from this guy! I'll be back! "

1821 tutors are online

### Other Documents

05/07/2015

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors