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, 744, 853 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 422, 744, 853 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 422, 744, 853 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, 744, 853 is 1.
HCF(422, 744, 853) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 422, 744, 853 is 1.
Step 1: Since 744 > 422, we apply the division lemma to 744 and 422, to get
744 = 422 x 1 + 322
Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 322 and 422, to get
422 = 322 x 1 + 100
Step 3: We consider the new divisor 322 and the new remainder 100, and apply the division lemma to get
322 = 100 x 3 + 22
We consider the new divisor 100 and the new remainder 22,and apply the division lemma to get
100 = 22 x 4 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 422 and 744 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(100,22) = HCF(322,100) = HCF(422,322) = HCF(744,422) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 853 > 2, we apply the division lemma to 853 and 2, to get
853 = 2 x 426 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 853 is 1
Notice that 1 = HCF(2,1) = HCF(853,2) .
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, 744, 853?
Answer: HCF of 422, 744, 853 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 422, 744, 853 using Euclid's Algorithm?
Answer: For arbitrary numbers 422, 744, 853 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.