# Divisibility

Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.

Correct result:

x =  1555

#### Solution:

x1: 4, 15, 26, 37, 48, 59, 70, 81, 92, 103, 114, 125, 136, 147, 158, 169, 180, 191, 202, 213, 224, 235, 246, 257, 268, 279, 290, 301, 312, 323, 334, 345, 356, 367, 378, 389, 400, 411, 422, 433, 444, 455, 466, 477, 488, 499, 510, 521, 532, 543, 554, 565, 576, 587, 598, 609, 620, 631, 642, 653, 664, 675, 686, 697, 708, 719, 730, 741, 752, 763, 774, 785, 796, 807, 818, 829, 840, 851, 862, 873, 884, 895, 906, 917, 928, 939, 950, 961, 972, 983, 994, 1005, 1016, 1027, 1038, 1049, 1060, 1071, 1082, 1093, 1104, 1115, 1126, 1137, 1148, 1159, 1170, 1181, 1192, 1203, 1214, 1225, 1236, 1247, 1258, 1269, 1280, 1291, 1302, 1313, 1324, 1335, 1346, 1357, 1368, 1379, 1390, 1401, 1412, 1423, 1434, 1445, 1456, 1467, 1478, 1489, 1500, 1511, 1522, 1533, 1544, 1555

x2: 10, 25, 40, 55, 70, 85, 100, 115, 130, 145, 160, 175, 190, 205, 220, 235, 250, 265, 280, 295, 310, 325, 340, 355, 370, 385, 400, 415, 430, 445, 460, 475, 490, 505, 520, 535, 550, 565, 580, 595, 610, 625, 640, 655, 670, 685, 700, 715, 730, 745, 760, 775, 790, 805, 820, 835, 850, 865, 880, 895, 910, 925, 940, 955, 970, 985, 1000, 1015, 1030, 1045, 1060, 1075, 1090, 1105, 1120, 1135, 1150, 1165, 1180, 1195, 1210, 1225, 1240, 1255, 1270, 1285, 1300, 1315, 1330, 1345, 1360, 1375, 1390, 1405, 1420, 1435, 1450, 1465, 1480, 1495, 1510, 1525, 1540, 1555

x3: 16, 35, 54, 73, 92, 111, 130, 149, 168, 187, 206, 225, 244, 263, 282, 301, 320, 339, 358, 377, 396, 415, 434, 453, 472, 491, 510, 529, 548, 567, 586, 605, 624, 643, 662, 681, 700, 719, 738, 757, 776, 795, 814, 833, 852, 871, 890, 909, 928, 947, 966, 985, 1004, 1023, 1042, 1061, 1080, 1099, 1118, 1137, 1156, 1175, 1194, 1213, 1232, 1251, 1270, 1289, 1308, 1327, 1346, 1365, 1384, 1403, 1422, 1441, 1460, 1479, 1498, 1517, 1536, 1555

$1555 \div 11 = 141 + \dfrac{ 4 }{ 11 } \ \\ 1555 \div 15 = 103 + \dfrac{ 10 }{ 15 } \ \\ 1555 \div 19 = 81 + \dfrac{ 16 }{ 19 } \ \\$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Do you solve Diofant problems and looking for a calculator of Diofant integer equations?

## Next similar math problems:

• Digit sum
Determine for how many integers greater than 900 and less than 1,001 has digit sum digit of the digit sum number 1.
• Divisors
The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers.
• Tissues
The store got three kinds of tissues - 132 children, 156 women and 204 men. Tissues each species were packed into boxes after the number of pieces the same for all three types (and greatest). Determine the number, if you know that every box has more than
• Numbers
Write smallest three-digit number, which in division 5 and 7 gives the rest 2.
• Red and white
Simona picked 63 tulips in the garden and tied bicolor bouquets for her girlfriends. The tulips were only red and white. She put as many tulips in each bouquet, three of which were always red. How much could Simon tear off white tulips? Write all the opti
• Remainder
A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
• Three-digit integers
How many three-digit natural numbers exist that do not contain zero and are divisible by five?
• Divisible by 5
How many three-digit odd numbers divisible by 5, which are in place ten's number 3?
• Four-digit number
Find also a four-digit number, which quadrupled written backwards is the same number.
• Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
• Ski tow
The ski club has 168 pupils and used lift with 60 seats, while students always follow the same sequence in filling seats. How many times while riding a ski lift skier sitting in the same seat as the first run?
• Divisors
Find all divisors of number 493. How many are them?
• Bundle of candies
In the store has 168 chocolates, caramel candies 224 and 196 hard candies. How many packages we can do and how many of candies will be in each package?