Learn 1: What does "Divisible" mean?
Imagine that you have 13 candy bars and 15 balloons. Can you divide them equally among 3 friends? You check if 13 and 15 are "divisible by" 3. This means when you divide, there is no remainder.
13 ÷ 3 = 4 R 1
Each friend gets 4 candy bars, but there is 1 left over (remainder).
15 ÷ 3 = 5 R 0
Each friend gets 5 balloons, with 0 left over (no remainder).
Conclusion: 15 is divisible by 3 because the remainder is 0. 13 is NOT divisible by 3 because the remainder is 1.
Learn 2: Divisibility Rules
Divisibility rules are shortcuts to check if a number is divisible by another without doing the full division!
Rule of 2
A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, 8).
Example: 12, 46, 780
Rule of 3
A number is divisible by 3 if the sum of its digits is divisible by 3.
Example: 93 (9+3=12, and 12 is divisible by 3).
Rule of 4
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Example: 284 (84 is divisible by 4).
Rule of 5
A number is divisible by 5 if its last digit is 0 or 5.
Example: 10, 45, 595
Rule of 6
A number is divisible by 6 if it is divisible by both 2 and 3.
Example: 630 (it's even, and 6+3+0=9).
Rule of 10
A number is divisible by 10 if its last digit is 0.
Example: 200, 30, 67,890
Example 1: Choose the correct answer
1. Which of the following is divisible by 2?
A. 61 B. 823 C. 374 D. 117
2. The number ______ is divisible by 3.
A. 335 B. 235 C. 1,175 D. 222
3. Which of the following is divisible by 4?
A. 3,016 B. 8,130 C. 8,014 D. 1,618
4. The number ______ is divisible by 5.
A. 2,400 B. 3,551 C. 54 D. 207
5. Which of the following is divisible by 2 and 5?
A. 115 B. 312 C. 725 D. 750
6. Which of the following is divisible by 3 and 5?
A. 130 B. 250 C. 75 D. 85
7. Which of the following is divisible by 2, 3 and 5?
A. 15 B. 30 C. 75 D. 320
8. The number ______ is divisible by 3 and 4.
A. 435 B. 524 C. 414 D. 228
9. Which of the following is divisible by 6?
A. 723 B. 110 C. 120 D. 130
10. Which of the following is divisible by 10?
A. 375 B. 312 C. 700 D. 7,002
Solution
1. C
2. D
3. A
4. A
5. D
6. C
7. B
8. D
9. C
10. C
Remarks
- Each whole number is divisible by 1.
- Each whole number except zero is divisible by itself.
- Zero is divisible by any whole number except itself.
Learn 3: The Link to Factors & Multiples
We know that 3 x 5 = 15. This simple equation tells us a lot!
This means "is a multiple of" is the same as "is divisible by".
- 15 is a multiple of 3, so 15 is divisible by 3.
- 15 is a multiple of 5, so 15 is divisible by 5.
- 3 and 5 are called factors of 15.
Generally
- If a number is a multiple of another number, then the first number is necessarily divisible by the second number.
- If a number is divisible by another number, then the first number is necessarily a multiple of the second number.
Example 2: Complete the Sentences
1. If 8 x 9 = 72, then 72 is divisible by ___ or ___.
2. If 36 is a multiple of 9, then 36 is ___ by 9.
3. If 412 is divisible by 4, then 4 is called a ___ of 412.
Solution
1. 8, 9
2. divisible
3. factor
Example 3: Choose the correct answer
1. Any ______ number is divisible by 2.
A. whole B. prime C. odd D. even
2. Any number is divisible by 3 if the sum of its digits is divisible by ______.
A. 2 B. 3 C. 5 D. 4
3. 235 is divisible by ______.
A. 2 B. 3 C. 5 D. 10
4. The number 1,132 is divisible by ______.
A. 4 B. 5 C. 6 D. 10
5. The number 801 is divisible by ______.
A. 10 B. 2 C. 3 D. 4
6. The number ______ is divisible by 3.
A. 1,123 B. 314 C. 410 D. 612
7. The number ______ is NOT divisible by 4.
A. 312 B. 520 C. 716 D. 434
8. 3,516 is NOT divisible by ______.
A. 3 B. 4 C. 5 D. 6
9. The number ______ is divisible by both 2 and 5.
A. 206 B. 425 C. 524 D. 620
10. The number ______ is divisible by 2 and 3.
A. 514 B. 632 C. 332 D. 444
11. The number ______ is divisible by both 4 and 5.
A. 200 B. 315 C. 210 D. 745
12. Which of the following is divisible by 2, 5, and 6?
A. 15 B. 256 C. 75 D. 30
13. The number ______ is divisible by 2, 3, 4 and 10.
A. 200 B. 600 C. 750 D. 636
14. The number ______ is divisible by 2, 3, 4, 5, 6 and 10.
A. 20 B. 30 C. 40 D. 60
15. If the Ones digit of a number is 0, then it is always divisible by ______.
A. 0 B. 3 C. 6 D. 10
16. Each whole number is divisible by ______.
A. 0 B. 1 C. 2 D. 5
Solution
1. D
2. B
3. C
4. A
5. C
6. D
7. D
8. C
9. D
10. D
11. A
12. D
13. B
14. D
15. D
16. B
Explore More Math Lessons
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