Highest Common Factor of 812, 522, 407 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 812, 522, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 812, 522, 407 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 812, 522, 407 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 812, 522, 407 is 1.
HCF(812, 522, 407) = 1
HCF of 812, 522, 407 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 812, 522, 407 is 1.
Highest Common Factor of 812,522,407 is 1
Step 1: Since 812 > 522, we apply the division lemma to 812 and 522, to get
812 = 522 x 1 + 290
Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 290 and 522, to get
522 = 290 x 1 + 232
Step 3: We consider the new divisor 290 and the new remainder 232, and apply the division lemma to get
290 = 232 x 1 + 58
We consider the new divisor 232 and the new remainder 58, and apply the division lemma to get
232 = 58 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 58, the HCF of 812 and 522 is 58
Notice that 58 = HCF(232,58) = HCF(290,232) = HCF(522,290) = HCF(812,522) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 407 > 58, we apply the division lemma to 407 and 58, to get
407 = 58 x 7 + 1
Step 2: Since the reminder 58 ≠ 0, we apply division lemma to 1 and 58, to get
58 = 1 x 58 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 58 and 407 is 1
Notice that 1 = HCF(58,1) = HCF(407,58) .
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Frequently Asked Questions on HCF of 812, 522, 407 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 812, 522, 407?
Answer: HCF of 812, 522, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 812, 522, 407 using Euclid's Algorithm?
Answer: For arbitrary numbers 812, 522, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.