What is the sum of all numbers less than 496 that devise evenly into
496
devise ----> divide
496 = 2*2*2*2*31
The 2's can be used in 5 ways, that is,
not take any
take 1
take 2
take 3
take all 4
the 31 can be used in 2 ways, either take or not take it
number of factors = 5*2 = 10
but that includes taking all or none
if we correspond to none as the factor 1 and if we take all we would get
496
the factors would be
1, 2, 4, 8, 16, 31, 62, 124, 248, and 496
Add them up
Thank you for the answer!
Thank you!!
Well, instead of giving you the sum, how about I throw in a little math joke? Why did the mathematician divide himself by 496? Because he couldn't find someone as evenly divisible as himself!
To find the sum of all numbers less than 496 that divide evenly into 496, we can follow these steps:
1. Identify the factors of 496: Factors are the numbers that divide evenly into a given number without leaving a remainder. Begin by finding the factors of 496. Start by dividing 496 by 2, as this is the smallest prime number. If the result is a whole number, then both the divisor and the result are factors. Repeat this process with progressively larger prime numbers until you reach the square root of 496. Note that if one factor is found, its corresponding factor can be determined by dividing the original number by the first factor.
2. List the factors: After identifying all the factors, make a list of them. Take into account that factors are typically listed in pairs.
3. Calculate the sum: Once the factors are listed, simply add them up to find the sum of all numbers less than 496 that divide evenly into it.
Following these steps, let's apply them to the number 496:
1. Identifying the factors of 496:
- Divide 496 by 2: 496 ÷ 2 = 248. Both 2 and 248 are factors.
- Divide 248 by 2: 248 ÷ 2 = 124. Both 2 and 124 are factors.
- Divide 124 by 2: 124 ÷ 2 = 62. Both 2 and 62 are factors.
- Divide 62 by 2: 62 ÷ 2 = 31. 31 is a prime number, so both 31 and 2 remain as factors.
- Divide 496 by 4 (2 x 2): 496 ÷ 4 = 124. Both 4 and 124 are factors.
- Divide 124 by 4: 124 ÷ 4 = 31. Both 4 and 31 are factors.
- Divide 496 by 8 (2 x 2 x 2): 496 ÷ 8 = 62. Both 8 and 62 are factors.
- Divide 62 by 8: 62 ÷ 8 = 7.75, which is not a whole number. Hence, 8 is not a factor.
2. Listing the factors:
The factors of 496 are: 1, 2, 4, 8, 31, 62, 124, and 496.
3. Calculating the sum:
Add all the factors together: 1 + 2 + 4 + 8 + 31 + 62 + 124 + 496 = 728.
Therefore, the sum of all numbers less than 496 that divide evenly into 496 is 728.