72 = 8x9 + 0 and 98 = 10x9 + 8 .
Change means increase or decrase.
In order to find the number of divisors we need to consider the powers of prime factors; we just add 1 to each power and we multiply them; i.e.
(2+1)x(2+1) = 3 x 3 = 9 gives the number of divisors since the number 36 = 2^{2} x 3^{2}.
Find the divisors of 36 and choose the ones having ...
This is a question asked in a mathematical competition. We hardened it a little bit. Congrats to who are able to solve .
The product of GCD and LCM should be the product of the numbers in question. So the elapsed times should be divisors of 36. These are given, the propers
are given, in the answer to question 5.
The case of 1 and 36 is not very likley but it does not change the answer. Have a look at ry1.
The product of the numbers is also the product of GCD and LCM. So the question is 60/2 = ?
The product of the numbers should be 200 .
GCD of 3 consecutive digits is being questioned. Let them be 1, 2 and 3 as a case .
5^{4} x n^{4} means it should have (4+1)x(4+1) = ... factors .
Two possible cases : Pairs are 1;18 or 2;9 . The pair 3;6 has 6 as LCM .
720 = 8x9x10 = 2^{3} x 3^{2} x 10 = 2^{4} x 3^{2} x 5 and the number of its divisors is 5x3x2 = 30 . For further help have
please a look at ry1.
The second should be 15. Since 17 is prime, the GCD is 1 .
Divisors of 150: 1,2,3,5,6,10,15,25,30,50,75,150
Divisors of 180: 1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
The number of divisors is 4x3x2 = 24 since 360=2^{3 x 32} x 5 .
The GCD is 6. For the group of 24 visitors 4 rooms are needed and ...
The number should be 56 190 .
We have derived in queation 12 of this test the divisors of 720; begin from there and find the divisors questioned. Look for help in ry1 .
The LCM is the product of the numbers because they are relatively prime .
LCM is clearly 7 and the GCD is 12x49 = 600 - 12 = 588 .
Division of these numbers by 4 gives 3 consecutives 10, 11 and 12 .
Begin with ry1 of question 18 and have a look at ry1 of this q. if needed .
Find the LCM of 27, 30 and 33.
(50 - 1) x 45 = ?
Two numbers are relatively prime if they do not have any common divisor .
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