Question

Find the greatest three-digit number which leaves remainders of 9,7, and 11, respectively when divided by 12, 10, and 14
a) 856 b) 961 c) 840 d) 837​

Answer 1

Step-by-step explanation:

A

900

(i)

75=3×5×5

45=3×3×5

60=2×2×3×5

For the greatest 3 digit number which divides by 75,45 and 60 leaves no remainder,

The number must be a multiple of 2×2×3×3×5×5=900

900 is the greatest 3− digit number that is divisible by 75,45, and 60

(ii)

Step 1 find L.C.M of given number

L.C.M of 75,45 and 60 is 900

step 2. find largest 3 digit number which is divisible by 900

largest 3 digit number which is divisible by 900 is itself 900

step 3 add the remainder to the number

900+4=904

Answer 2

Answer:

837/12

the remainder is 9

the quotient is 69

837/14

the remainder is 11

the quotient is 67

837/10

the remainder is 7

the quotient is 83