HCF of 16, 88, 223, 874 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 16,88,223,874 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(16,88,223,874).

Here 88 is greater than 16

Now, consider the largest number as 'a' from the given number ie., 88 and 16 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 88 > 16, we apply the division lemma to 88 and 16, to get

88 = 16 x 5 + 8

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 8 and 16, to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 16 and 88 is 8

Notice that 8 = HCF(16,8) = HCF(88,16) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Here 223 is greater than 8

Now, consider the largest number as 'a' from the given number ie., 223 and 8 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 223 > 8, we apply the division lemma to 223 and 8, to get

223 = 8 x 27 + 7

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 7 and 8, to get

8 = 7 x 1 + 1

Step 3: We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 223 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(223,8) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Here 874 is greater than 1

Now, consider the largest number as 'a' from the given number ie., 874 and 1 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 874 > 1, we apply the division lemma to 874 and 1, to get

874 = 1 x 874 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 874 is 1

Notice that 1 = HCF(874,1) .

Therefore, HCF of 16,88,223,874 using Euclid's division lemma is 1.