2.4: Some Interesting Facts about Division
- be able to recognize a whole number that is divisible by 2, 3, 4, 5, 6, 8, 9, or 10
Division by 2, 3, 4, and 5
A whole number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
The numbers 80, 112, 64, 326, and 1,008 are all divisible by 2 since the last digit of each is 0, 2, 4, 6, or 8, respectively.
The numbers 85 and 731 are
not
divisible by 2.
A whole number is divisible by 3 if the sum of its digits is divisible by 3.
The number 432 is divisible by 3 since 4 + 3 + 2 = 9 and 9 is divisible by 3.
\(432 \div 3 = 144\)
The number 25 is not divisible by 3 since \(2 + 5 = 7\), and 7 is not divisible by 3.
A whole number is divisible by 4 if its last two digits form a number that is divisible by 4.
The number 31,048 is divisible by 4 since the last two digits, 4 and 8, form a number, 48, that is divisible by 4.
\(31048 \div 4 = 7262\)
The number 137 is not divisible by 4 since 37 is not divisible by 4.
A whole number is divisible by 5 if its last digit is 0 or 5.
The numbers 65, 110, 8,030, and 16,955 are each divisible by 5 since the last digit of each is 0 or 5.
Practice Set A
State which of the following whole numbers are divisible by 2, 3, 4, or 5. A number may be divisible by more than one number.
26
- Answer
-
2
Practice Set A
81
- Answer
-
3
Practice Set A
51
- Answer
-
3
Practice Set A
385
- Answer
-
5
Practice Set A
6,112
- Answer
-
2, 4
Practice Set A
470
- Answer
-
2, 5
Practice Set A
113,154
- Answer
-
2, 3
Division by 6, 8, 9, 10
A number is divisible by 6 if it is divisible by both 2 and 3.
The number 234 is divisible by 2 since its last digit is 4. It is also divisible by 3 since 2 + 3 + 4 = 9 and 9 is divisible by 3. Therefore, 234 is divisible by 6.
The number 6,532 is
not
divisible by 6. Although its last digit is 2, making it divisible by 2, the sum of its digits, 6 + 5 + 3 + 2 = 16, and 16 is not divisible by 3.
A whole number is divisible by 8 if its last three digits form a number that is divisible by 8.
The number 4,000 is divisible by 8 since 000 is divisible by 8.
The number 13,128 is divisible by 8 since 128 is divisible by 8.
The number 1,170 is
not
divisible by 8 since 170 is not divisible by 8.
A whole number is divisible by 9 if the sum of its digits is divisible by 9.
The number 702 is divisible by 9 since 7 + 0 + 2 is divisible by 9.
The number 6588 is divisible by 9 since 6 + 5 + 8 + 8 = 27 is divisible by 9.
The number 14,123 is
not
divisible by 9 since 1 + 4 + 1 + 2 + 3 = 11 is not divisible by 9.
A Whole number is divisible by 10 if its last digit is 0.
The numbers 30, 170, 16,240, and 865,000 are all divisible by 10.
Practice Set B
State which of the following whole numbers are divisible 6, 8, 9, or 10. Some numbers may be divisible by more than one number.
900
- Answer
-
6, 9, 10
Practice Set B
6,402
- Answer
-
6
Practice Set B
6,660
- Answer
-
6, 9, 10
Practice Set B
55,116
- Answer
-
6, 9
Exercises
For the following 30 problems, specify if the whole number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10. Write "none" if the number is not divisible by any digit other than 1. Some numbers may be divisible by more than one number.
Exercise \(\PageIndex{1}\)
48
- Answer
-
2, 3, 4, 6, 8
Exercise \(\PageIndex{2}\)
85
Exercise \(\PageIndex{3}\)
30
- Answer
-
2, 3, 5, 6, 10
Exercise \(\PageIndex{4}\)
83
Exercise \(\PageIndex{5}\)
98
- Answer
-
2
Exercise \(\PageIndex{6}\)
972
Exercise \(\PageIndex{7}\)
892
- Answer
-
2, 4
Exercise \(\PageIndex{8}\)
676
Exercise \(\PageIndex{9}\)
903
- Answer
-
3
Exercise \(\PageIndex{10}\)
800
Exercise \(\PageIndex{11}\)
223
- Answer
-
none
Exercise \(\PageIndex{12}\)
836
Exercise \(\PageIndex{13}\)
665
- Answer
-
5
Exercise \(\PageIndex{14}\)
4,381
Exercise \(\PageIndex{15}\)
2,195
- Answer
-
5
Exercise \(\PageIndex{16}\)
2,544
Exercise \(\PageIndex{17}\)
5,172
- Answer
-
2, 3, 4, 6
Exercise \(\PageIndex{18}\)
1,307
Exercise \(\PageIndex{19}\)
1,050
- Answer
-
2, 3, 5, 6, 10
Exercise \(\PageIndex{20}\)
3,898
Exercise \(\PageIndex{21}\)
1,621
- Answer
-
none
Exercise \(\PageIndex{22}\)
27,808
Exercise \(\PageIndex{23}\)
45,764
- Answer
-
2, 4
Exercise \(\PageIndex{24}\)
49,198
Exercise \(\PageIndex{25}\)
296,122
- Answer
-
2
Exercise \(\PageIndex{26}\)
178,656
Exercise \(\PageIndex{27}\)
5,102,417
- Answer
-
none
Exercise \(\PageIndex{28}\)
16,990,792
Exercise \(\PageIndex{29}\)
620,157,659
- Answer
-
none
Exercise \(\PageIndex{30}\)
457,687,705
Exercises for Review
Exercise \(\PageIndex{31}\)
In the number 412, how many tens are there?
- Answer
-
1
Exercise \(\PageIndex{32}\)
Subtract 613 from 810.
Exercise \(\PageIndex{33}\)
Add 35, 16, and 7 in two different ways.
- Answer
-
(35 + 16) + 7 = 51 + 7 = 58
(35 + (16 + 7) = 35 + 23 = 58
Exercise \(\PageIndex{34}\)
Find the quotient \(35 \div 0\), if it exists.
Exercise \(\PageIndex{35}\)
Find the quotient. \(3654 \div 42\).
- Answer
-
87