Hi vinviper1,
h(100) = 2*4*...*100 ==> (1*2) * (2*2) * (3*2)...(50*2)
From the above breakdown, every prime number under 50 (<= 49) is a factor of h(100).
Now h(100)+1 will have none of the prime numbers under 50 (<=49) as a factor.
Think about this, 3 is a factor 6, 3 is not a factor of 6+1 or 6+2. Need to wait for 6+3 for the next multiple.
5 is a factor 10, 5 is not a factor of 10+1, 10+2, 10+3 or 10+4. Need to wait for 10+5 for the next multiple.
If N is a multiple of prime factor F, N+F is the next multiple of F.
So we are left with prime factors greater than 49.
Cheers
gmat prep prime numbers
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