Question

2419! = (504)^a *b. b is not a multiple of 7?​

Answer 1

Answer:

573'5499:67,?97"/4"4-

Answer 2

Answer:

a = 402

Step-by-step explanation:

504 can be factorized as (2^3 x 3^2 x 7)

So the effectively the question now becomes (2^3 x 3^2 x 7)^a x b. Where we need to find the value of a.

We now need to figure out what maximum power of 7 can be present in 2419! as 7 will have a lot less powers as compared to 2 or 3. This is done by continuously dividing 2419! by 7 and only looking at the quotients (This is done until we get a quotient smaller than 7)

2419!/7 = 345 (Quotient), 345/7 = 49 (Quotient), 49/7 = 7(Quotient), 7/7 = 1 (Quotient)

Then add 345+49+7+1 = 402.

This whole process shows us what maximum power of 7 can be present. Since b is not a power of 7 we don't need to worry about that.