**Division when divisor is near to the Base of 10 power**

This division method work if divisor is near to the base like 10, 100, 1000 etc. Here **Nikhilam sutra of vedic maths** is useful.

We can also call it **Base method of division**. Because we apply it when the divisor is near the base of power 10.

I explained it by taking lots of different sums, its really a **very easy & interesting way of doing division.**

**Case 1: When divisor is near to base 10**

Here we solve the sums when divisor is near to the base 10 like, 8, 7, 6 etc. We can apply same method for divisor 9 also. But I already publish a blog that explain the __shortcut division trick for divisor 9__.

Now onward we use abbreviations,

**R = Remainder**

**Q = Quotient**

**Diff. = Difference**

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**Ex i) 23 ÷ 8**

**Step 1: Identify Base & Difference**

As divisor is 8, which is near to 10, so Base = 10

Diff. = base – number = 10 – 8 = 2

**Step 2**: Split the dividend in to two parts (Q & R) in such a way that Number of digit in remainder side is equal to number of zero in base.

**Base: 10**

**Divisor = 8**

**diff. = 2**

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** ****As here Base 10 have 1 zero so in remainder side, we take 1 digit**

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**Step 3:**Take 2 down as it is at quotient place. This is our first digit of Q.** **

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**Step 4: **Now multiply this 2 with diff. 2.

So, 2 x 2 = 4 & add this 4 in next digit of dividend i.e. 3 & write down the total at R place**.**

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**Answer, Q = 2 & R = 7**

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**Ex. ii) 112 ÷ 7 **

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**Base 10**

**Div. = 7 **

**Diff. = 3 **

As remainder side answer is 14, which is greater than 7(divisor) is not advisable. So, we re-divide the R.

14 ÷ 7, Q = 2, R = 0

**Addition of both Q is our final Q****. **

**Q = 14 + 2 = 16, & R = 0**

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**Case ii)When divisor is near to the base 100, 1000, 10000 etc.**

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**Ex. iii) 1324 ÷ 98 **

**Base: 100 **(As 98 is close to 100)

**Divisor: 98**

**Diff. =100-98 =02**

**Step 1: **Divide the dividend in two parts Q & R. **In R side we take 2 digit as base is 100.** We take 1 as it is in Q place.

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**Step2: **Multiply 1 with diff. 02 & add this in next two digits

1 x 02 = 02

**As divisor have 2- digits so, we consider 2 digits to add (02 instead of 2)**

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**We add here second digit** ** i.e. 3+0=3**

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**Step 3: **Now multiply this 3 with diff. 02 = 06

**Add this result from third digit of dividend**. Now all digits are cover, so we add up the numbers.** **

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In remainder last digit is 4 + 6 = 10,** so we carry-over 1 in left hand side digit** i.e. 4 + 1 = 5, so R = 50.

**Answer, Q = 13 & R = 50. **

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**Ex. iv) 711 ÷ 96**

**Base = 100 **

**Divisor = 96 **

**Diff. = 04 **

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**Answer, Q = 7 & R = 39**

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**Ex. v) 1431 ÷ 88 **

**Base = 100 **

**Divisor = 88 **

**Diff. = 12 **

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Here, Q = 15 & R = 111 > divisor(88)

So, we re-divide it, 111 ÷ 88, Q = 1, R = 23

**So, Final Q = 15 + 1 = 16 & R = 23 **

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**Ex. vi) 210021 ÷ 8888 **

**Base = 10000 **

**Divisor = 8888 **

**Diff. = 1112 **

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** Q = 23, R = 5597**

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**Case iii) When divisor is greater than base**

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**Ex. vii) 1962 ÷ 112**

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**Step 1: **As we do in previous sum find out diff.

**Base = 100** (As divisor is close to 100)

**Divisor = 112**

**Diff. = -(12)** (Base – divisor)

**Step 2: **Divide the dividend in two parts (Q part & R part)**. In R side we take 2 digit as base is 100. **

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**Step 3: **First digit 1 we take in Q place as it is & for next step, we multiply it with diff. –(12) & **add the result from second digit of dividend.**

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**Step 4: **Now multiply second digit of Q (8) with diff. 8 x -(12) = -(96) & **add them from third digit of dividend.**

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** **Here, Q = 18 & R = -(54)

**But -ve remainder is not advisable, so we reduce Q by 1 & subtract the remainder from the divisor. **

Q = 18 -1 =17 & R = 112 – 54 =58

**Answer Q = 17 & R = 58**

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**Ex. viii) 120887 ÷ 1**** **

**Base =1000 **

**Divisor = 1212 **

**Diff. = -(212) **

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Q = 100 + 00 -1 = 99** (By using place value) **& Q = 899

**Answer, Q = 99 & R = 899 **

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**Ex. ix) 1129 ÷ 108 **

** Base = 100 **

**Divisor = 108 **

**Diff. = -(08) **

** **** **

Q = 11, R = -60 + 1 = -59

**But -ve remainder is not advisable, so we reduce Q by 1 & subtract the remainder from the divisor. **

**Q = 11 -1 = 10, R = 108 – 59 = 49**

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** Find this links to study more:**

1. Division trick when divisor is 9

2. Multiply 99 x 96, 9998 x 9982… in 3 seconds by Base method

3. Find the cube & cube root of perfect cube number by very easy way

4. What is Vedic Mathematics & 16- Sutras

5. Find the square & square – root of any number by very easy way

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