Question

a) Find the greatest number that divides 45, 60 and 75 without leaving remainder​

Answer 1

Step-by-step explanation:

75=5×5×345=5×3×360=5×2×3×2

As we can see that the number has to be divisible by 75 so, we need two 5 and one 3,

5×5×3

Now for 45 we need one 5 and two 3, but we already have one 5 and one 3 in 5×5×3 so, we will multiply our number with just 3.

After multiplying we get,

5×5×3×3

Now for the number to be divisible by 60 we already have 5 and 3 in 5×5×3×3 , so we just need two 2.

After multiplying 5×5×3×3 by two 2 we get,

5×5×3×3×2×2=900

Now 900 is the smallest number that gives no remainder when divided by 75, 45, 60.

But it is also the largest 3 – digit number that gives no remainder when divided by 75, 45, 60.

Hence for (a) 900 is the correct answer.

Now we will proceed to part (b).

For the part (b) we will add 4 to 900 which gives 904.

And we know that 900 is divisible by 75, 45, 60 so, 904 will give us the required remainder 4 when divided by each number.

Hence, 904 is the correct answer for (b).

Note: One thing that we need to understand is how the smallest number that gives no remainder when divided by 75, 45, 60 is also the largest 3 – digit number that gives no remainder when divided by 75, 45, 60.

$hope \: \: it \: helps \: you$

Answer 2

900

45=3×3×5

60=2×2×3×5

75=3×5×5

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

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