Highest Common Factor of 121, 200, 222 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 121, 200, 222 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 121, 200, 222 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 121, 200, 222 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 121, 200, 222 is 1.

HCF(121, 200, 222) = 1

HCF of 121, 200, 222 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 121, 200, 222 is 1.

Highest Common Factor of 121,200,222 using Euclid's algorithm

Highest Common Factor of 121,200,222 is 1

Step 1: Since 200 > 121, we apply the division lemma to 200 and 121, to get

200 = 121 x 1 + 79

Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 79 and 121, to get

121 = 79 x 1 + 42

Step 3: We consider the new divisor 79 and the new remainder 42, and apply the division lemma to get

79 = 42 x 1 + 37

We consider the new divisor 42 and the new remainder 37,and apply the division lemma to get

42 = 37 x 1 + 5

We consider the new divisor 37 and the new remainder 5,and apply the division lemma to get

37 = 5 x 7 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 121 and 200 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(37,5) = HCF(42,37) = HCF(79,42) = HCF(121,79) = HCF(200,121) .

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

Step 1: Since 222 > 1, we apply the division lemma to 222 and 1, to get

222 = 1 x 222 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 222 is 1

Notice that 1 = HCF(222,1) .

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Frequently Asked Questions on HCF of 121, 200, 222 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 121, 200, 222?

Answer: HCF of 121, 200, 222 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 121, 200, 222 using Euclid's Algorithm?

Answer: For arbitrary numbers 121, 200, 222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.