Fewer than 500 sheep,

There are fewer than 500 sheep, but if they stand in a double, triple, quadruple, five and sixth order, one sheep will remain.
But they can stand in the seventh order. How many are sheep?

Result

n =  301

Solution:

a%b = a modulo b

n=7: n%2=1, n%3=1, n%4=3, n%5=2, n%6=1, n%7=0
n=14: n%2=0, n%3=2, n%4=2, n%5=4, n%6=2, n%7=0
n=21: n%2=1, n%3=0, n%4=1, n%5=1, n%6=3, n%7=0
n=28: n%2=0, n%3=1, n%4=0, n%5=3, n%6=4, n%7=0
n=35: n%2=1, n%3=2, n%4=3, n%5=0, n%6=5, n%7=0
n=42: n%2=0, n%3=0, n%4=2, n%5=2, n%6=0, n%7=0
n=49: n%2=1, n%3=1, n%4=1, n%5=4, n%6=1, n%7=0
n=56: n%2=0, n%3=2, n%4=0, n%5=1, n%6=2, n%7=0
n=63: n%2=1, n%3=0, n%4=3, n%5=3, n%6=3, n%7=0
n=70: n%2=0, n%3=1, n%4=2, n%5=0, n%6=4, n%7=0
n=77: n%2=1, n%3=2, n%4=1, n%5=2, n%6=5, n%7=0
n=84: n%2=0, n%3=0, n%4=0, n%5=4, n%6=0, n%7=0
n=91: n%2=1, n%3=1, n%4=3, n%5=1, n%6=1, n%7=0
n=98: n%2=0, n%3=2, n%4=2, n%5=3, n%6=2, n%7=0
n=105: n%2=1, n%3=0, n%4=1, n%5=0, n%6=3, n%7=0
n=112: n%2=0, n%3=1, n%4=0, n%5=2, n%6=4, n%7=0
n=119: n%2=1, n%3=2, n%4=3, n%5=4, n%6=5, n%7=0
n=126: n%2=0, n%3=0, n%4=2, n%5=1, n%6=0, n%7=0
n=133: n%2=1, n%3=1, n%4=1, n%5=3, n%6=1, n%7=0
n=140: n%2=0, n%3=2, n%4=0, n%5=0, n%6=2, n%7=0
n=147: n%2=1, n%3=0, n%4=3, n%5=2, n%6=3, n%7=0
n=154: n%2=0, n%3=1, n%4=2, n%5=4, n%6=4, n%7=0
n=161: n%2=1, n%3=2, n%4=1, n%5=1, n%6=5, n%7=0
n=168: n%2=0, n%3=0, n%4=0, n%5=3, n%6=0, n%7=0
n=175: n%2=1, n%3=1, n%4=3, n%5=0, n%6=1, n%7=0
n=182: n%2=0, n%3=2, n%4=2, n%5=2, n%6=2, n%7=0
n=189: n%2=1, n%3=0, n%4=1, n%5=4, n%6=3, n%7=0
n=196: n%2=0, n%3=1, n%4=0, n%5=1, n%6=4, n%7=0
n=203: n%2=1, n%3=2, n%4=3, n%5=3, n%6=5, n%7=0
n=210: n%2=0, n%3=0, n%4=2, n%5=0, n%6=0, n%7=0
n=217: n%2=1, n%3=1, n%4=1, n%5=2, n%6=1, n%7=0
n=224: n%2=0, n%3=2, n%4=0, n%5=4, n%6=2, n%7=0
n=231: n%2=1, n%3=0, n%4=3, n%5=1, n%6=3, n%7=0
n=238: n%2=0, n%3=1, n%4=2, n%5=3, n%6=4, n%7=0
n=245: n%2=1, n%3=2, n%4=1, n%5=0, n%6=5, n%7=0
n=252: n%2=0, n%3=0, n%4=0, n%5=2, n%6=0, n%7=0
n=259: n%2=1, n%3=1, n%4=3, n%5=4, n%6=1, n%7=0
n=266: n%2=0, n%3=2, n%4=2, n%5=1, n%6=2, n%7=0
n=273: n%2=1, n%3=0, n%4=1, n%5=3, n%6=3, n%7=0
n=280: n%2=0, n%3=1, n%4=0, n%5=0, n%6=4, n%7=0
n=287: n%2=1, n%3=2, n%4=3, n%5=2, n%6=5, n%7=0
n=294: n%2=0, n%3=0, n%4=2, n%5=4, n%6=0, n%7=0
n=301: n%2=1, n%3=1, n%4=1, n%5=1, n%6=1, n%7=0 <<<<<<=====

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