Answer:
hcf=(1,605; 600) = 3 × 5
Step-by-step explanation:
Prime Factorization of a number: finding the prime numbers that multiply together to make that number.
1,605 = 3 × 5 × 107;
1,605 is not a prime, is a composite number;
600 = 23 × 3 × 52;
600 is not a prime, is a composite number;
* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.
Multiply all the common prime factors, by the lowest exponents (if any).
gcf, hcf, gcd (1,605; 600) = 3 × 5
gcf, hcf, gcd (1,605; 600) = 3 × 5 = 15;
The numbers have common prime factors.
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Look at the attached picture for the correct process.
This can be solved by a contingency table to enumerate all possibilities.
1 2 3 4 5 6 7 8 9
1 - 1 2 3 4 5 6 7 8
2 1 - 1 2 3 4 5 6 7
3 2 1 - 1 2 3 4 5 6
4 3 2 1 - 1 2 3 4 5
5 4 3 2 1 - 1 2 3 4
6 5 4 3 2 1 - 1 2 3
7 6 5 4 3 2 1 - 1 2
8 7 6 5 4 3 2 1 - 1
9 8 7 6 5 4 3 2 1 -
The diagonal entries are void because we cannot pick two tags with the same number. We count 72 outcomes (excluding diagonal) and 12 of them are threes. Therefore
Probability that the difference is 3 = 12/72 = 1/6