What is the greatest number that divides 145 , 266 and 315 leaving a remainder 1,2 and 3 respectively?
Answers
Answer:
24 is the greatest number that divides 145, 266, 315 leaving a remainder 1, 2, 3 respectively.
Step-by-step explanation:
After dividing 145 by the number, remainder is 1
∴ The number devides 145-1=144 perfectly,
similarly, for 266, remainder is 2, and for 315 reminder is 3
∴ 266 - 2 = 264
315 - 3 = 312
∴ 144, 264 & 312 are the numbers perfectly divisible by the common number
Factorising each number
144 = 3 x 3 x 2 x 2 x 2 x 2
264 = 11 x 3 x 2 x 2 x 2
312 = 13 x 3 x 2 x 2 x 2
As we can see from the factors, 3 x 2 x 2 x 2 are the factors common for all three numbers
∴ 3 x 2 x 2 x 2 = 24
∴ 24 is the greatest number that divides 145, 266, 315 leaving a remainder 1, 2, 3 respectively
Answer:
Step-by-step explanation:
The first step, subtract the remainders from each number respectively.
For 145, the remainder is 1, subtracting 1 from 145 gives 144.
145-1 =144
for 226, the remainder is 2. subtracting 2 from 226 gives 224
226- 2= 224
For 315, the remainder is 3, subtracting 3 from 315 gives 312
315- 3= 312
to find the number that divides all the number giving the remainders, the greatest common divider is obtained.
find the G.C.D of 144,224,312
To find the G.C.D, factorize the numbers.
This is :
144= 2^4×3^2
224=2^5×7
312=2^3×3×13
Therefore, the G.C.D is 2^3= 8. the number that divides all of them giving the remainders respectively is 8.
Answer: 8