2!, 3!, 4!, etc. carry:=0; % Start a multiply by n. for i:=1 to last do % Step along every digit. d:=digit[i]*n + carry; % The classic multiply. digit[i]:=d mod Base; % The low-order digit of the result. carry:=d div Base; % The carry to the next digit. next i; while carry > 0 % Store the carry in the big number. if last >= Limit then croak("Overflow!"); % If possible! last:=last + 1; % One more digit
3/15 is less than 4/7.
12 is the only number which satisfies this. Multiples of 4 are: 4, 8, 12, 16, . . . .
It is 28 because 4*7 = 28
Every prime number except 2 must be odd. This is because if it were even it would be divisible by 2 and so wouldn't be a prime number. The next point to note is that all odd numbers are one more or one less than a multiple of 4. Because 2 more than a multiple of 4 is even, and 3 more than a multiple of 4 is the same as 1 less than the multiple of 4 above. Thus every prime number except 2 must be 1 more or 1 less than a multiple of 4.
12
The multiple of 4 less than 15 is 12. A multiple is the result of multiplying a number by an integer. In this case, 4 multiplied by 3 equals 12, which is less than 15. Therefore, the multiple of 4 less than 15 is 12.
989. If there is a remainder of 2 when divided by 3, the number is one less than a multiple of 3. If there is a remainder of 4 when divided by 5, the number is one less than a multiple of 5. Thus the number required is one less than a multiple of the lowest common multiple of 3 and 5 (that is 15). So what is needed is an even multiple of 15 less than or equal to 1000: 1000 ÷ 15 = 662/3 Thus the highest even multiple of 15 not greater than 1000 is 66 x 15 = 990, and the required number is 989.
3/15 is less than 4/7.
12 is the only number which satisfies this. Multiples of 4 are: 4, 8, 12, 16, . . . .
The multiples of 4 that are less than 30 are 4, 8, 12, 16, 20, 24, 28. So the greatest multiple of 4 that is less than 30 is 28.
As 100 = 4 x 25 the biggest multiple of 4 less than 100 is 4 x (25 -1) = 96
It is 28 because 4*7 = 28
4 x 5 = 20
Every prime number except 2 must be odd. This is because if it were even it would be divisible by 2 and so wouldn't be a prime number. The next point to note is that all odd numbers are one more or one less than a multiple of 4. Because 2 more than a multiple of 4 is even, and 3 more than a multiple of 4 is the same as 1 less than the multiple of 4 above. Thus every prime number except 2 must be 1 more or 1 less than a multiple of 4.
12
3,7,11,19,23,31,43,47,51,59,67,71,79...
60