Investigate the questions in parts a and b by considering a number of examples
a. If a whole number is divisible both by 6 and by 2, is it necessarily divisible by 12?
b. If a whole number is divisible both by 3 and by 4, is it necessarily divisible by 12?
c. based on your examples, what do you think the answers to the questions in a and b should be?
d. Based on your answer to part c, determine whether 3,321,297,402,348,516 is divisible by 12 without using a calculator or doing long division. Explain your reasoning.
Hello, ihavvaquestion!
No . . .(a) If a whole number is divisible both by 6 and by 2, is it necessarily divisible by 12?
As chiph588@ pointed out, 6 is divisible by 6 and by 2,
. . but it is not divisible by 12.
Yes . . .b. If a whole number is divisible both by 3 and by 4, is it necessarily divisible by 12?
If a number is multiple of 3 and a multiple of 4, it is a multiple of 12.
Um . . . "No" and "Yes" ?c. Based on your examples, what do you think
the answers to the questions in (a) and (b) should be?
d. Based on your answer to part (c), determine whether
. . is divisible by 12 without using a calculator or doing long division.
. . Explain your reasoning.
A number is divisible by 3 if the sum of its digits is divisible by 3.
Since ,
. . which is divisible by 3, then is divisible by 3.
A number is divisible by 4 if its last two-digit number is divisible by 4.
Since ends in , which is divisible by 4, then is divisible by 4.
Therefore, is divisible by both 3 and 4 . . . is divisible by 12.