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 460, 712, 422 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 460, 712, 422 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 460, 712, 422 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 460, 712, 422 is 2.
HCF(460, 712, 422) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 460, 712, 422 is 2.
Step 1: Since 712 > 460, we apply the division lemma to 712 and 460, to get
712 = 460 x 1 + 252
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 252 and 460, to get
460 = 252 x 1 + 208
Step 3: We consider the new divisor 252 and the new remainder 208, and apply the division lemma to get
252 = 208 x 1 + 44
We consider the new divisor 208 and the new remainder 44,and apply the division lemma to get
208 = 44 x 4 + 32
We consider the new divisor 44 and the new remainder 32,and apply the division lemma to get
44 = 32 x 1 + 12
We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get
32 = 12 x 2 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 460 and 712 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(44,32) = HCF(208,44) = HCF(252,208) = HCF(460,252) = HCF(712,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 422 > 4, we apply the division lemma to 422 and 4, to get
422 = 4 x 105 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 422 is 2
Notice that 2 = HCF(4,2) = HCF(422,4) .
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 460, 712, 422?
Answer: HCF of 460, 712, 422 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 460, 712, 422 using Euclid's Algorithm?
Answer: For arbitrary numbers 460, 712, 422 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.