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?

Correct answer:

n =  301

Step-by-step explanation:

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 <<<<<<=====

We will be pleased if You send us any improvements to this math problem. Thank you!


Tips to related online calculators
Do you want to calculate least common multiple two or more numbers?
Do you want to perform natural numbers division - find the quotient and remainder?

Related math problems and questions:

  • Sheep
    ships Shepherd tending the sheep. Tourists asked him how much they have. The shepherd said, "there are fewer than 500. If I them lined up in 4-row 3 remain. If in 5-row 4 remain. If in 6-row 5 remain. But I can form 7-row." How many sheep have herdsman?
  • Shepherd
    sheep_1 The shepherd has fewer than 500 sheep; where they can be up to 2, 3, 4, 5, 6 row is always 1 remain, and as can be increased up to 7 rows of the sheep, and it is not increased no ovine. How many sheep has a shepherd?
  • Plums
    svestka In the bowl are plums. How many would be there if we can divide it equally among 8, 10 and 11 children?
  • Athletes
    olympics_4 Athletes at the stadium could enter two-steps, three-steps, four-steps, five-steps, six-steps. There were more than 100 but less than 200. How many athletes were there?
  • Spartakiada
    spartakiada_1 Practitioners lined up in rectangle with row with four, five or six exercisers, one always missing to full rectangle. How many exercisers were on the field, if they have estimated not been more than 100?
  • LCM
    calc_icon What is the least common multiple of 5, 50, 14?
  • Lcm simple
    lcm_gears Find least common multiple of this two numbers: 140 175.
  • Lcm of three numbers
    prime What is the Lcm of 120 15 and 5
  • Dance group
    dancers The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
  • On Children's
    bonbons_13 On Children's Day, the organizers bought 252 chewing gums, 396 candies and 108 lollipops. They want to make as many of the same packages as possible. Advise them what to put in each package and how many packages they can make this way.
  • Meadow
    ovce-miestami-baran On the meadow grazing horses, cows, and sheep, together with less than 200. If cows were 45 times more, horses 60 times more, and sheep 35 times more than there are now, their numbers would equally. How many horses, cows, and sheep are on the meadow toget
  • School
    ziaci_6 Less than 500 pupils attend school. When it is sorted into pairs, one pupil remains. Similarly, when sorted into 3, 4, 5 and 6 members team one remains. Sorted to seven members teams, no left behind. How many pupils are attending this school?
  • School year
    zosity At the beginning of the school year, 396 notebooks and 252 textbooks are ready to be distributed in the classroom. All pupils receive the same number of notebooks and the same amount of textbooks. How many pupils are there in the class if you know that th
  • The King
    gold_4 The King wants to divide his sons equally. He has 42 rubies and 45 diamonds. How many sons and how will they share them?
  • The florist
    ruze_6 The florist had 200 roses in the morning. During the day, more than half sold it. From the remaining roses, it will tie the bouquet. If a bouquet of 3, 4, 5, or 6 roses are bound, one always remains. How many roses from the morning shipment sold?
  • Tiles
    100dlazdic How many tiles of 20 cm and 30 cm can build a square if we have a maximum of 100 tiles?
  • Trees in alley
    tree_6 There are four trees in the alley between which the distances are 35m, 15m and 95m. Trees must be laid in the spaces so that the distance is the same and the maximum. How many trees will they put in and what will be the distance between them?