Thank you for visiting Find the greatest number that will divide 330 647 and 829 leaving remainders of 15 17 and 19 respectively. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The greatest number that will divide 330, 647, and 829 leaving remainders 15, 17, and 19 is 11.
1. List the prime factors of the 3 numbers:
330 = 2 x 3 x 5 x 11
647 = 3 x 7 x 23
829 = 17 x 7 x 11
2. Find the maximum numbers of times each prime number appears in the 3 numbers:
2 appears once
3 appears twice
5 appears once
7 appears twice
11 appears twice
17 appears once
23 appears once
3. Multiply the maximum numbers of times each prime number appears:
2 x 3 x 5 x 7 x 11 x 17 x 23 = 11,220,700
4. Divide 11,220,700 by 11:
11,220,700 ÷ 11 = 1,020,100
5. Check the remainders:
1,020,100 ÷ 330 = 3,098 remainder 15
1,020,100 ÷ 647 = 1,575 remainder 17
1,020,100 ÷ 829 = 1,230 remainder 19
6. Since all remainders are correct, 11 is the greatest number that will divide 330, 647, and 829 leaving remainders 15, 17, and 19.
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