Option 1
From the numbers 387, 756, 829, 2,148 write down the numbers which are evenly divisible:
1) by 2; 2) by 9.
2. Decompose 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) 15 and 8; 3) 16 and 12.
5. Prove that the numbers 272 and 1,365 are mutually prime.
6. Replace the asterisk in the notation 1 52* by digits such that the resulting number is a multiple of 3 (consider all possible cases).
7. Petya arranged books equally on 12 shelves and then moved them, also equally, to 8 shelves. How many books did Petr have, if he knows that there were more than 100 books, but less than 140?
Option 2
From the numbers 405, 972, 865, 2,394 write down the numbers, which are divisible by integers:
1) by 5; 2) by 9.
2. Decompose the number 1 176 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. Prove that numbers 297 and 304 are mutually prime.
6. Replace the asterisk in the notation 1 99* with digits such that the resulting number is a multiple of 3 (consider all possible cases).
7. A farmer can put the harvested apples equally into baskets of 12 kg or into boxes of 15 kg. How many kilograms of apples did the farmer gather, if he knows that there were more than 150 kg of apples, but less than 200 kg?
