Page 123 - NUMINO Challenge_C2
P. 123
14 Overs and Shorts
Basic Concepts Remainder
If a number divided by 3 or 5 has the same remainder (the number that is
left over or that lacks), that number is equal to a number added to or
subtracted from a common multiple of 3 and 5.
For example, if the remainder of a number divided by 3 and 5 is 1, that
number is 1 greater than a common multiple of 3 and 5.
(common multiple of 3 and 5) 1 16, 31, 46,
If the remainder of a number divided by 3 is 1 and when divided by 5 is 3,
that number is 2 less than a common multiple of 3 and 5.
(common multiple of 3 and 5) 2 13, 28, 43,
Example Find the least 3-digit number that has a remainder of 2 when
divided by both 3 and 7.
Class Notes
A number that does not leave a remainder when divided by both 3 and 7 is a
of 3 and 7.
A number that leaves a remainder of 2 when divided by both 3 and 7 is 2 greater than
a common multiple of 3 and 7: 23, 44, , , ,.
Therefore, the least 3-digit number that meets the conditions is .
Try It Again When a number is divided by 4, the remainder is 3 and when
the same number is divided by 6, the remainder is 5. Find the
least 2-digit number that meets the conditions.
120 NUMINO Challenge C2
Basic Concepts Remainder
If a number divided by 3 or 5 has the same remainder (the number that is
left over or that lacks), that number is equal to a number added to or
subtracted from a common multiple of 3 and 5.
For example, if the remainder of a number divided by 3 and 5 is 1, that
number is 1 greater than a common multiple of 3 and 5.
(common multiple of 3 and 5) 1 16, 31, 46,
If the remainder of a number divided by 3 is 1 and when divided by 5 is 3,
that number is 2 less than a common multiple of 3 and 5.
(common multiple of 3 and 5) 2 13, 28, 43,
Example Find the least 3-digit number that has a remainder of 2 when
divided by both 3 and 7.
Class Notes
A number that does not leave a remainder when divided by both 3 and 7 is a
of 3 and 7.
A number that leaves a remainder of 2 when divided by both 3 and 7 is 2 greater than
a common multiple of 3 and 7: 23, 44, , , ,.
Therefore, the least 3-digit number that meets the conditions is .
Try It Again When a number is divided by 4, the remainder is 3 and when
the same number is divided by 6, the remainder is 5. Find the
least 2-digit number that meets the conditions.
120 NUMINO Challenge C2
