**OPTION 1**

№ 1

Which of the numbers 5, 12, 45, 60, 135, 180, 387, 405, 703, 756, 8290, are divided evenly:

1) by 2; 2) by 3 3) by 5?

№ 2

Decompose the number 756 into prime factors.

№ 3

Find the greatest common divisor of the numbers:

1) 24 and 54 2) 72 and 264.

№ 4

Find the least common multiple of the numbers:

1) 16 and 32; 2) 8 and 15; 3) 16 and 12.

№ 5

Determine whether the numbers 62 and 95 are mutually prime.

№ 6

Instead of an asterisk in the notation of 152*, write such a digit that the resulting number is a multiple of: 1) 5; 2) 3 (consider all possible cases)

№ 7

They bought 315 chocolate candies and 720 caramel candies for presents. What is the largest number of gifts that can be made up if each gift has the same number of chocolates and caramel candies?

№ 8*

What is the smallest number of soldiers marching on the parade ground if they can be lined up in a formation of 75 in a row or in a formation of 63 in a row?

№ 9*

Find the value of the expression and write out all the divisors of this number:

8,9-5,1 + 2,562:4,2.

№ 10*

Write in ascending order all correct fractions with a denominator of 7 in which the numerator and denominator are mutually prime numbers.

№ 11*

Solve the equation: (63x – 219) : 6 + 66 = 439.

**OPTION 2**

№ 1

Which of the numbers 4, 17, 68, 104, 136, 255, 492, 675, 3258, 7030, are divided evenly:

1) by 2; 2) by 9 3) by 5?

№ 2

Decompose the number 780 into prime factors.

№ 3

Find the greatest common divisor of the numbers:

1) 27 and 36 2) 168 and 252.

№ 4

Find the least common multiple of the numbers:

1) 11 and 33; 2) 9 and 10; 3) 18 and 12.

№ 5

Determine whether the numbers 64 and 85 are mutually prime.

№ 6

Instead of an asterisk in the entry of 823*, write such a digit that the resulting number would be a multiple of: 1) 2; 2) 9 (consider all possible cases)

№ 7

During the first shift, the camp had 1,080 campers, and during the second shift, 336 campers. What is the highest number of people that could have been in a troop if there were the same number of people in each troop on both shifts?

№ 8*

Between the two settlements there were poles every 200 meters. They decided to replace these poles so that the distance between adjacent poles would be 84 m. What is the smallest possible distance between the two points if it is not necessary to replace the first and the last post?

№ 9*

Find the value of the expression and write out all the divisors of this number:

5,8-6,8 + 2,632:4,7.

№ 10*

Write in ascending order all irregular fractions with a numerator of 6 in which the numerator and the denominator are mutually prime numbers.

№ 11*

Solve the equation: (35x + 305) : 9 – 14 = 191.