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 422, 274, 912 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 422, 274, 912 is 2 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 422, 274, 912 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 422, 274, 912 is 2.
HCF(422, 274, 912) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 422, 274, 912 is 2.
Step 1: Since 422 > 274, we apply the division lemma to 422 and 274, to get
422 = 274 x 1 + 148
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 148 and 274, to get
274 = 148 x 1 + 126
Step 3: We consider the new divisor 148 and the new remainder 126, and apply the division lemma to get
148 = 126 x 1 + 22
We consider the new divisor 126 and the new remainder 22,and apply the division lemma to get
126 = 22 x 5 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 422 and 274 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(126,22) = HCF(148,126) = HCF(274,148) = HCF(422,274) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 912 > 2, we apply the division lemma to 912 and 2, to get
912 = 2 x 456 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 912 is 2
Notice that 2 = HCF(912,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 422, 274, 912?
Answer: HCF of 422, 274, 912 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 422, 274, 912 using Euclid's Algorithm?
Answer: For arbitrary numbers 422, 274, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.