Highest Common Factor of 382, 74712 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 382, 74712 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 382, 74712 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 382, 74712 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 382, 74712 is 2.
HCF(382, 74712) = 2
HCF of 382, 74712 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 382, 74712 is 2.
Highest Common Factor of 382,74712 is 2
Step 1: Since 74712 > 382, we apply the division lemma to 74712 and 382, to get
74712 = 382 x 195 + 222
Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 222 and 382, to get
382 = 222 x 1 + 160
Step 3: We consider the new divisor 222 and the new remainder 160, and apply the division lemma to get
222 = 160 x 1 + 62
We consider the new divisor 160 and the new remainder 62,and apply the division lemma to get
160 = 62 x 2 + 36
We consider the new divisor 62 and the new remainder 36,and apply the division lemma to get
62 = 36 x 1 + 26
We consider the new divisor 36 and the new remainder 26,and apply the division lemma to get
36 = 26 x 1 + 10
We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 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 382 and 74712 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(62,36) = HCF(160,62) = HCF(222,160) = HCF(382,222) = HCF(74712,382) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 382, 74712 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 382, 74712?
Answer: HCF of 382, 74712 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 382, 74712 using Euclid's Algorithm?
Answer: For arbitrary numbers 382, 74712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
