Aricent Divisibility Quiz-1

(3 × 5)^12 × (2 × 7)^10 × (10)^25
= (3)¹² × (5)¹² × (2)¹⁰ × (7)¹⁰ × (2)²⁵ × (5)²⁵
= (3)¹² × (5)¹²⁺²⁵ × (2)¹⁰⁺²⁵ × (7)¹⁰
= (3)¹² × (5)³⁷ × (2)³⁵ × (7)¹⁰
Now, it cannot be further factorised hence this is the prime factorisation of the above number.
So, (3)¹² × (5)³⁷ × (2)³⁵ × (7)¹⁰ has total
12 + 37 + 35 + 10 = 94 prime factors.

The least possible value is 3

The number nearest to 15207 is 15411

Write factors of 7936

2*2*2*2*2*2*2*2*31
now make pairs for squares

4*4*4*4*31
you will 31 without pair

just multiply 31 with 7936 to get 246016

The remainder = 16
So, the divisor = 16 × 5 = 80
The quotient is 1/20 of the divisor = 80/20 = 4
For any division, dividend = (divisor × quotient) + remainder
In this case :- (80 × 4) + 16
⇒ 320 + 16
= 336
So, the number is 336

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If the number is divisible by 85 rem=0 then by 17 also there will be 0

44100 is the answer...
.because it is divisible by all Nd a perfect squar

The greatest number = H.C.F of (138-63), (228-138), (228-63)
H.C.F of 75, 90, 165 = 15.
15 is the greatest number.

90 x 80 x 70 x 60 x 50 x 40 x 30 x 20 x 10

=> (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) = 10^9

=> 5^10

Hence,

10 is the highest power of 5.

The question is, how many powers of 5 are in the factors of 30! (that's 30 factorial, for those above)...

Only the numbers 5, 10, 15, 20, 25, and 30 have divisors of 5. And 25 is divisible by 5^2.

So the answer is 5*5*5*5*(5^2)*5 = 5^7.

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