Question

What is the maximum value of m, if the number N = 90*42*324*55 is divisible by 3 power m

Answer 1

Answer:

m = 7

Step-by-step explanation:

What is the maximum value of m, if the number N = 90*42*324*55 is divisible by 3 power m

N = 90*42*324*55

Separate out factors of 3 from each numbers

90 = 3 * 30 = 3 * 3 * 10

42 = 3 * 14

324 = 3 * 108 = 3 * 3 * 36 = 3 * 3 * 3 * 12 = 3 * 3 * 3 * 3 * 4

55 = no factor of 3

N = (3 * 3 * 10)(3 * 14)(3 * 3 * 3 * 3 * 4)(55)

=> N = (3 * 3 * 3 * 3 * 3 * 3 * 3)(10)(14)(4) (55)

=> N = 3⁷ * (10)(14)(4) (55)

N is divisible by  3^m

maximum value of m = 7