What is the largest number that will divide 90207, 232585 and 127986 without leaving a remainder? A. 257
Answers
Answer:
Step-by-step explanation:
Whenever you get questions like this focus on the smallest number of them and try to find out some common properties like divisibility rules.
the smallest number here is 90207 and since its digits sum is divisible by 9 the number is divisible by 9 but the others are not. so eliminate 9. when you divide 90207 by 9 you will get 10023 as quotient. this number is divisible by 3 but the others are not. eliminate 3 when you divide 10023 by 3 you will get 3341 as the quotient. try to divide one of the numbers by 3341 if it does not give a remainder try the other if that too does not give a remainder than the required number is 3341. if any one of the numbers gives a remainder try to split 3341
This 3341 becomes difficult to split. use some easy divisibilty properties of numbers like 13 add 4 times of 1 to 334 and see if it divisible by 13. since 338 is divisible by 13, 3341 is divisible by 13 and the quotient is 257.
257 divides the other two numbers and hence the answer is 257