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P Pankaj Sanodiya
Since it is the smallest number of such type, it will be the product of 4 smallest prime numbers. that is  2 3  5 7 = 210

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P Pankaj Sanodiya
45 = 5  9 Factors of 5 = 1, 5 Factors of 9 = 1. 3, 9 Therefore, 5 and 9 are co-prime numbers. Since the last digit of 25110 is 0. it is divisible by 5. Sum of the digits of 25110 = 2 + 5 + 1 +1 + 0 = 9 As the sum of the digits of 25110 is divisible by 9, therefore. 25110 is divisible by 9. Since the number is divisible by 5 and 9 both, it is divisible by 45.

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P Pankaj Sanodiya
in factorization, we don't write composite numbers. All the factors should be prime numbers in this method.  (a) 24 = 2 3 4  As we know that 4 is a composite number.  Hence This is not a prime factorization.  b) 56 = 7 2 2 2 In this factorization, all the factors of 56 are prime numbers. There is no composite number.  Hence This is prime factorization.  c) 70 = 2 5  7  In this...

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P Pankaj Sanodiya
3+5=8, which is divisible by 4 15+17=32, which is divisible by 4 19+21=40, which is divisible by 4  

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P Pankaj Sanodiya
  2 3 4=24, which is divisible by 6 9 10 11=990, which is divisible by 6 20 21 22=9240, which is divisible by 6  

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P Pankaj Sanodiya
Prime factors of 1729 are -7,13,19. Ascending order =7<13<19. Relation = 7,13,19 differ by 6

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P Pankaj Sanodiya
Smallest five-digit number = 10,000 10000 = 2 2 2 2 5 5 5 5

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P Pankaj Sanodiya
Greatest four-digit number = 9999 9999 = 3  3 11 101

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P Pankaj Sanodiya
1 is the factors which are not especially included in the prime factorization of a composite number. When the number is divisible by 2 co-prime numbers then they are divisible by their product.  When two given numbers are divisible by a number, the sum is also divisible by number. When 2 given numbers are divisible by number then its difference is divisible by that number.
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