Find numbers between 120 and 140 that are divisible by 8. Also find numbers between 1120 and 1140, and 3120 and 3140, that are divisible by 8. What do you observe?

Question

Homi · Accepted Answer

We will find numbers that can be divided by 8 without any leftover.

Step 1 — Finding numbers between 120 and 140

We need to find numbers from 120 up to 140. Let us start by checking 120. We divide 120 by 8.

$120 \div 8$ $= 15$

$\boxed{\text{120 is divisible by 8}}$

So, 120 is our first number. To find the next number, we add 8 to 120.

$120 + 8$ $= 128$

$\boxed{\text{128 is divisible by 8}}$

So, 128 is our second number. To find the next number, we add 8 to 128.

$128 + 8$ $= 136$

$\boxed{\text{136 is divisible by 8}}$

So, 136 is our third number. If we add 8 again, we get $136 + 8 = 144$ . This number 144 is bigger than 140, so we stop. The numbers between 120 and 140 that are divisible by 8 are 120, 128, 136.

Step 2 — Finding numbers between 1120 and 1140

We need to find numbers from 1120 up to 1140. Let us start by checking 1120. We divide 1120 by 8.

$1120 \div 8$ $= 140$

$\boxed{\text{1120 is divisible by 8}}$

So, 1120 is our first number. To find the next number, we add 8 to 1120.

$1120 + 8$ $= 1128$

$\boxed{\text{1128 is divisible by 8}}$

So, 1128 is our second number. To find the next number, we add 8 to 1128.

$1128 + 8$ $= 1136$

$\boxed{\text{1136 is divisible by 8}}$

So, 1136 is our third number. If we add 8 again, we get $1136 + 8 = 1144$ . This number 1144 is bigger than 1140, so we stop. The numbers between 1120 and 1140 that are divisible by 8 are 1120, 1128, 1136.

Step 3 — Finding numbers between 3120 and 3140

We need to find numbers from 3120 up to 3140. Let us start by checking 3120. We divide 3120 by 8.

$3120 \div 8$ $= 390$

$\boxed{\text{3120 is divisible by 8}}$

So, 3120 is our first number. To find the next number, we add 8 to 3120.

$3120 + 8$ $= 3128$

$\boxed{\text{3128 is divisible by 8}}$

So, 3128 is our second number. To find the next number, we add 8 to 3128.

$3128 + 8$ $= 3136$

$\boxed{\text{3136 is divisible by 8}}$

So, 3136 is our third number. If we add 8 again, we get $3136 + 8 = 3144$ . This number 3144 is bigger than 3140, so we stop. The numbers between 3120 and 3140 that are divisible by 8 are 3120, 3128, 3136.

Step 4 — Making an observation

Let us look at all the numbers we found. For the first group: 120, 128, 136. For the second group: 1120, 1128, 1136. For the third group: 3120, 3128, 3136. We can see that the numbers that can be divided by 8 are always 8 apart. The pattern of these numbers is similar in all three groups.

Answer

(i) Numbers divisible by 8 between 120 and 140: 120, 128 and 136. (ii) Numbers divisible by 8 between 1120 and 1140: 1120, 1128 and 1136. (iii) Numbers divisible by 8 between 3120 and 3140: 3120, 3128 and 3136. (iv) Observation: The numbers that can be divided by 8 are always 8 apart. The pattern of these numbers is similar in all three groups.

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