LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

FINDING HCF BY DIVISION METHOD

**TO FIND HCF By
DIVISION METHOD**

**Divide the bigger
number by the smaller/smallest number. If there is no reminder then the smaller
number is the HCF. If there is a reminder, take it as the new divisor and take the
previous divisor as the new dividend. Continue step 2 until there is no
reminder. The last divisor is the required HCF.**

__Example
-1__

**Find
the HCF of 224 & 336**

**Ans.) We take
the smallest number between given numbers 224 & 336 as Divisor and another
would be considered as Dividend. So, 224 is Divisor and 336 is Dividend to be
considered –**

**Step.1–**** we divide 336 by 224 and we find 112 as**** a ****reminder.**

**Step.2–**** We
consider reminder 112 as Divisor and**** ****previously ****taken Divisor 224 would be considered as
Dividend in**** the ****next**** ****step.**

**Step.3–**** we
divide Dividend 224 by Divisor 112 and ****get
Quotient 2 and reminder Zero ‘0’. The process ****would
have continued until the reminder becomes zero ****‘0’.**

**So, the
HCF of two given numbers 224 & 336 would be 112. (Ans.)**

__Example
-2__

**Find
the HCF of 308 & 420**

**Ans.) We take the
smallest number between given numbers 308 & 420 as Divisor and
another would be considered as Dividend. So, 308 is Divisor and 420 is Dividend to be considered –**

__Step.1__**- We divide 420 by 308 and we find 112
as a reminder.**

__Step.2–__** We consider reminder 112 as Divisor
and previously taken Divisor 308 would be considered as Dividend in the next step.**

__Step.3–__** We find 84 as a reminder and now 84
would be considered as Divisor and previously taken Divisor
112 would be considered as Dividend now. The same process will be
repeated until the reminder to be found Zero ‘0’. **

__Step.4 –__** We find 28 as a
reminder and it is to be considered now as divisor and previously taken
Divisor 84 would be considered as Dividend. **

__Step.5–__** Now we find 3 as Quotient and obtained
reminder is Zero ‘0’.**

**So, the HCF of two
given numbers 308 & 420 would be 28 (Ans.)**

__Example– 3__

**Find
the greatest number (HCF) of 528, 1296 & 1120**

**Ans.) We will take
the two smallest numbers between given numbers 528, 1296 & 1120, so we will
take 528 as Divisor and 1120 would be considered as Dividend. So, 528 is
Divisor and 1120 is Dividend to be considered –**

__Step.1–__** We divide 1120 by 528 and we find 64
as a reminder.**

__Step.2–__** Now we consider 64 as a divisor and
earlier divisor 528 to be ****considered as a
dividend. Now we get 16 as a reminder.**

__Step.3__**–**** Now we consider 16 as Divisor and
earlier divisor 64 to be considered as dividends. The same process will be continued until we find the reminder as Zero ‘0’**

__Step.4-__** Now we find quotient 4 and reminder
zero ‘0’. ****The HCF
of 528 & 1120 is = 16, now we will find the HCF between 16 & 1296.**

__Step.5–__
consider 16 as divisor and 1296 as dividend.

__Step.6–__ here we
find that, 81 as quotient and **reminder is Zero ‘0’. **

**The HCF of 16 &
1296 is 16, so the HCF of 528, 1296 & 1120 is 16. (Ans.)**

__Example– 4__

**Find
the greatest number (HCF) of 456, 2128 & 1140**

**Ans.) We will take
the two smallest numbers between given numbers 456, 2128 & 1140 so we will
take 456 as Divisor and 1140 would be considered as Dividend. So, 456 is Divisor
and 1140 is Dividend to be considered –**

**Step.1–**** We divide 1140 by 456 and find
the reminder 228.**

**Step.2–**** Now,
we consider reminder 228 as divisor and 456 ****as dividend and we**** Zero
‘0’ reminder. ****So, 228 is the HCF of
1140 & 456**

**The HCF of 456 & 1140 is = 228, now we will find the HCF between 228
& 2128**

**Step.3-**** We will take obtained HCF of 1140
& 456 which is 228 as divisor and consider 2128 as dividend and we
find 76 as a reminder**

**Step.4 –**** We will consider
reminder 76 as divisor and previous divisor 228 is considered as dividend
and we found Zero ‘0’ as a reminder.**

**HCF of the numbers
228 & 2128 is 76. (Ans.)**