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?

Correct answer:

n =  301

Step-by-step explanation:

n<500 (n1)3 (n1)4 (n1)5 (n1)6 n7 3 ...  prime number 4=22 5 ...  prime number 6=23 LCM(3,4,5,6)=2235=60  n0=LCM(3,4,5,6)=60  n1=1 n0+1=1 60+1=61 t1=n1/7=61/7=761=8758.7143  n2=2 n0+1=2 60+1=121 t2=n2/7=121/7=7121=177217.2857  n3=3 n0+1=3 60+1=181 t3=n3/7=181/7=7181=257625.8571  n4=4 n0+1=4 60+1=241 t4=n4/7=241/7=7241=347334.4286  n5=5 n0+1=5 60+1=301 t5=n5/7=301/7=43  n6=6 n0+1=6 60+1=361 t6=n6/7=361/7=7361=517451.5714  n7=7 n0+1=7 60+1=421 t7=n7/7=421/7=7421=607160.1429  n8=8 n0+1=8 60+1=481 t8=n8/7=481/7=7481=687568.7143  n=5 n0+1=5 60+1=301  d3=(n1)/3=(3011)/3=100 d4=(n1)/4=(3011)/4=75 d5=(n1)/5=(3011)/5=60 d6=(n1)/6=(3011)/6=50 d7=n/7=301/7=43

Did you find an error or inaccuracy? Feel free to write us. Thank you!


Tips to related online calculators
Do you want to calculate least common multiple two or more numbers?
Do you solve Diofant problems and looking for a calculator of Diofant integer equations?

Related math problems and questions: