What is the least number which when divided by 27, 35, 45, and 49 leaves a remainder of 6 in each case?
Factors of27 = 3x3x335 = 5x745 = 3x3x549 = 7x7LCM = 3x3x3x5x7x7 = 6615Add 6 to 6615 to get 6621 as the answer.Check: 6621/27 = quotient of 245 and a remainder of 6. Correct.6621/35 = quotient of 189 and a remainder of 6. Correct.6621/45 = quotient of 147 and a remainder of 6. Correct.6621/49 = quotient of 135 and a remainder of 6. Correct.
How do I find a number which when divided by 2, 3, 4, 5, 6, 7, 8, 9, 10 individually gives a remainder of 1 and when divided by 11 gives a remainder 0?
you will have to find out the LCM of all the number given ie from 2 to 10. the LCM will be divisible by all the numbers 2 to 10. Because you will have to get a reminder of 1 add 1 to the LCM and check whether that number is divisible by 11, if not multiply the LCM by 2 and add 1 and check if it is divisible by 11, if not continue like this till LCM*n + 1 is divisible by 11The LCM of 2 to 10 is 2520 Add 1 to 2520 which will be 2521. 2521 is not divisible by 11Continuing like this 2520*2 + 1 = 5041 not divisible by 112520*3 + 1 = 7561 not divisible2520 * 4 = 5040 + 1 = 5041 not divisible2520 * 5 = 12600 + 1 = 12601 not divisible2520*6 = 15120 + 1 = 15121 not divisible2520 * 7 = 17640 + 1 = 17641 not divisible2520 * 8 = 20160 + 1 = 25161 not divisible2520 * 9 = 22680 + 1 = 22681 not divisible2520 * 10 - 25200 + 1 = 25201 Divisible by 11I have explained a similar question in a video
What are the 7 types of intelligence quotients (IQ)?
IQ is a measure of a composite of your willingness to co-operate in an IQ test and you ability to do an IQ test. The IQ test measures your ability to do IQ tests which does not have much relationship to anything else.There is as many or as few classifications of IQ as you like because like phrenology they are all bullshit. 1, 2 3, 4, 7, 1007? It all does not matter. What is important is what you do with your intelligence.Read up about the track-record of IQ and you will realise that it is all nonsense and has sinister eugenic and social engineering undertones. If you are really intelligent you will refuse to be tested. I was tested without my consent or consent of my parents. I refused to co-operate and drew aeroplanes and submarines on them.
By which number can you divide 1,757,051 to get a remainder of zero?
1757051 has two prime factors: 1291 and 1361.So, in total, it has 4 divisors: 1, 1291, 1361 and 1757051. Divide it by any of the numbers here and you’d get a remainder of 0.To get the prime factors of any number, you can try the site mention in the link below, type the number and hit Go.http://numbermatics.com/
How do I find the remainder when a number is divided by a number ranging from 1 to 9?
Here's a quick list - Note, these may not be conventional methods; they are just simple play of numbers and their properties, that I just thought of as soon as I saw your question.Divisor: Clue to find remainder- 1: Always 0- 2: Of course, if it's even then 0 else 1- 3: Add the digits till you get a single digit number. The remainder of that result when divided by 3 is your answer.- 4: If the number is even, divide it by 2, if you get an even number then the remainder is 0 else 2. If the number is odd, divide the next number by 2, if you get an even number then the remainder is 3 else its 1- 5: If the last digit is greater than or equal to 5 subtract 5 from it to get the remainder. If it's less than 5, that's your remainder.- 6: If it's an even number, then add the digits till you get a single digit number and the remainder of that answer when divided by 6. If it's an odd number do the same thing for the next number and finally subtract 1 from the remainder you get.- 7: I'm beat here - I would usually round it off to the nearest multiple of 10 check the divisibility/remainder, then work my way through.- 8: Find the remainder when divided by 4. Then subtract this from the number and divide the number by 4 - if the quotient is even then the initial remainder is the answer, if the the quotient is odd then add 4 to the initial remainder. - 9: Add all the digits till you get a single digit. The result is your remainder (if it's 9 then your remainder is 0).Hope these help.
How do I show that an integer and its cube gives the same remainder when divided by 6?
According to Euclid's division lemmaa=bq+r where r < bAcc. to question let b=6Then r=0,1,2,3,4,5Possible cases for the value of a=6q,6q+1,6q+2,6q+3,6q+4,6q+5Case 1:a=6q (gives 0 as remainder when divided by 6)On cubing both sidesa^3 = 216 q^3 (gives 0 as remainder when divided by 6)Case 2:a=6q +1 (gives 1 as remainder when divided by 6)On cubing both sidesa^3 = 216 q^3 + 108q^2 + 18q +1a^3 = 6(36q^3 + 18q^2 + 3q) +1a^3 = 6m+1 (gives 1 as remainder when divided by 6)Case 3:a=6q +2 (gives 2 as remainder when divided by 6)On cubing both sidesa^3 = 216 q^3 + 216q^2 + 72q +8a^3 = 6(36q^3 + 36q^2 + 12q +1) +2a^3 = 6m+2 (gives 2 as remainder when divided by 6)Case 4:a=6q +3 (gives 3 as remainder when divided by 6)On cubing both sidesa^3 = 216 q^3 + 324q^2 + 162q +27a^3 = 6(36q^3 + 54q^2 + 27q+4) +3a^3 = 6m+3 (gives 3 as remainder when divided by 6)Case 5:a=6q +4 (gives 4 as remainder when divided by 6)On cubing both sidesa^3 = 216 q^3 + 432q^2 + 288q +64a^3 = 6(36q^3 + 72q^2 + 48q+10) +4a^3 = 6m+4 (gives 4 as remainder when divided by 6)Case 6:a=6q +5 (gives 5 as remainder when divided by 6)On cubing both sidesa^3 = 216 q^3 + 540q^2 +450 q +125a^3 = 6(36q^3 + 90q^2 + 75q+20) +5a^3 = 6m+5 (gives 5 as remainder when divided by 6)Therefore an integer and its cube gives the same quotient when divided by 6.
How do I calculate change of rate of volume?
a.Take the first derivative of V = (4/3) π r^3 w.r.t r, we getVolume change = dV/dr = 4π r^2Put r =1 ft,dV/dr = 4π (2)^2dV/dr = 16π (Answer)b.First of all, we have to find volume at r=2 ft and r=2.2 ft. We will use V = (4/3) π r^3 equation.At r = 2 ft, V1 = (4/3) π 2^3 = (32/3) π = 33.51 cubic ft.At r = 2.2 ft V2 = (4/3) π 2.2^3 = (32/3) π = 44.60 cubic ft.So the volume change is V2 - V1 = 44.60 - 33.51 = 11.09 cubic ft.