Which set of factors of the number 420 has the least possible sum? Which set of factors of the. Number 420 has the greatest possible sum? Be sure that the two sets of factors both have a product of 420
2 + 2 + 5 + 7 + 3 = 19
210 + 2 = 212
To find the set of factors with the least possible sum for a given number, you need to find the factors of the number and arrange them in a way that minimizes their sum. Similarly, to find the set of factors with the greatest possible sum, you need to arrange the factors in a way that maximizes their sum.
Let's start by finding the factors of the number 420. To do this, you can divide 420 by numbers starting from 1 and continuing until you reach half of the number:
1: 420 ÷ 1 = 420
2: 420 ÷ 2 = 210
3: 420 ÷ 3 = 140
4: 420 ÷ 4 = 105
5: 420 ÷ 5 = 84
6: 420 ÷ 6 = 70
7: 420 ÷ 7 = 60
8: 420 ÷ 8 = 52
9: 420 ÷ 9 = 46
10: 420 ÷ 10 = 42
So, the factors of 420 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 20, 21, 28, 30, 35, 40, 42, 60, 70, 84, 105, 140, 210, 420.
Now, to find the set of factors with the least possible sum that also has a product of 420, you need to consider the divisors that are close to each other. In this case, the factors 2 and 210 have the lowest possible sum at 212.
To find the set of factors with the greatest possible sum that adds up to 420, you need to consider the largest and smallest factors, which are 1 and 420. Therefore, the set 1, 420 has the greatest possible sum at 421.
In summary:
- The set of factors with the least possible sum and a product of 420 is {2, 210} with a sum of 212.
- The set of factors with the greatest possible sum and a product of 420 is {1, 420} with a sum of 421.