1. Fill in the blanks.

1.a and b are both natural numbers. If a÷b= 10, the greatest common divisor of A and B is (), and the least common multiple is ().

2. The greatest common divisor of A, B, A and B is ()× () = (), and the smallest common multiple of A and B is ()× ()× () = ().

3. The common divisor of all natural numbers is ().

4. If m and n are prime numbers, then their greatest common divisor is () and their least common multiple is ().

5.4, 9, 10 and 16, of which () and () are prime numbers, () and () are prime numbers.

6. Divide 15 and 30 by a number, which is exactly divisible. The maximum quantity is ().

*7. The sum of two consecutive natural numbers is 2 1, the greatest common divisor of these two numbers is (), and the least common multiple is ().

*8. The sum of two adjacent odd numbers is 16. Their greatest common divisor is () and their least common multiple is ().

**9. When a number is divisible by 3, 5 and 7, it is 1, and the minimum number is ().

10. Write two prime numbers according to the following requirements.

(1) Two prime numbers (). (2) Two consecutive natural numbers () and ().

(3) Arbitrary natural numbers () and (). (4) Two composite numbers () and ().

(5) Odd numbers and odd numbers () and (). (6) Odd and even numbers () and ().

2. True or false.

1. The coprime of two numbers must be both prime numbers. ( )

2. Two different odd numbers must be prime numbers. ( )

3. The smallest prime number is the common divisor of all even numbers. ( )

4. Two numbers with common divisor 1 must be prime numbers. ( )

5.a is a prime number and B is also a prime number, so it must be a prime number. ( )

3. Directly say the greatest common divisor and the least common multiple of each group number.

26 and 13 () () 13 and 6 () () 4 and 6 () ()

5 and 9 () () 29 and 87 () () 30 and 15 () ()

13, 26 and 52 () () 2, 3 and 7 () ()

4. Find the greatest common divisor and the least common multiple of each group of numbers below. (Only the least common multiple of three numbers)

45 and 60 () () 36 and 60( )() 27 and 72 () ()

76 and 80( )() 42, 105 and 56 () 24, 36 and 48 ()

* * 5. Think about it:

The school bought 40 ballpoint pens and 50 exercise books, which were awarded to the third-class students in grade four on average. As a result, there are four more ballpoint pens and two more exercise books. There are several third-class students in the fourth grade. What prize did they win?

Test answer

1. Fill in the blanks.

1.a and b are both natural numbers. If a÷b= 10, the greatest common divisor of a and b is (b) and the least common multiple is (a).

2. The greatest common divisor of A, B, A and B is (2) × (3) = (6), and the smallest common multiple of A and B is (2) × (3) × (5) × (7) = (2 10.

The common divisor of all natural numbers is (1).

4. If m and n are prime numbers, their greatest common divisor is (1) and their least common multiple is (mn).

5. Among the four numbers 4, 9, 10 and 16, (4) and (9) are prime numbers, (9) and (10) are prime numbers.

6. Divide 15 and 30 by a number, which is exactly divisible. The maximum number is (15).

*7. The sum of two consecutive natural numbers is 2 1, the greatest common divisor of these two numbers is (1), and the least common multiple is (1 10).

*8. The sum of two adjacent odd numbers is 16, their greatest common divisor is (1), and their smallest common multiple is (63).

**9. When a certain number is divisible by 3, 5 and 7, it is 1, and the minimum number is (106).

10. Write two prime numbers according to the following requirements.

(1) Two prime numbers (2) and (3).

(2) Two consecutive natural numbers (4) and (5).

(3) 1 and arbitrary natural numbers (1) and (9).

(4) Two composite numbers (9) and (16).

(5) Odd numbers and odd numbers (15) and (7).

(6) Odd and even numbers (7) and (4).

2. True or false.

1. The coprime of two numbers must be both prime numbers. (×)

2. Two different odd numbers must be prime numbers. (×)

3. The smallest prime number is the greatest common divisor of all even numbers. (√)

4. Two numbers with common divisor 1 must be prime numbers. (×)

5.a is a prime number and B is also a prime number, so it must be a prime number. (×)

3. Directly say the greatest common divisor and the least common multiple of each group number.

26 and13 (13,26)13 and 6 (1 78) 4 and 6 (2, 12).

5 and 9 (1, 45) 29 and 87 (29, 87) 30 and 15 (15, 30)

13,26 and 52 (13,52) 2,3 and 7( 1 42)

4. Find the greatest common divisor and the least common multiple of each group of numbers below. (Only the least common multiple of three numbers)

The greatest common divisor of 45 and 60 is 15 and the least common multiple is 180.

The greatest common divisor of 36 and 60 is 12 and the least common multiple is 180.

The greatest common divisor of 27 and 72 is 9 and the least common multiple is 2 16.

The greatest common divisor of 76 and 80 is 4, and the least common multiple is 1520.

The least common multiple of 42, 105 and 56 is 840.

The least common multiple of 24, 36 and 48 is 144.

* * 5. Think about it:

The school bought 40 ballpoint pens and 50 exercise books, which were awarded to the third-class students in grade four on average. As a result, there are four more ballpoint pens and two more exercise books. There are several third-class students in the fourth grade. What prize did they win?

Is that what you think?

(1) There are four more ballpoint pens, indicating that (one) ballpoint pen is used.

(2) There are two exercise books, that is, the exercise book (this one).

(3) The common divisor of 36 and 48 is 2,3,4,6, 12.

Because, 2 does not meet the requirements.

, 3 does not meet the requirements

4. Not qualified.

6 eligible

, 12 meets the requirements.

So the number of three good students in grade four is 6 or 12.

(4) When the number of miyoshi students is 6, each student has 6 ballpoint pens and 8 exercise books;

When the number of "Three Good Students" is 12, each student will have three ballpoint pens and four exercise books.