Highest Common Factor of 670, 1229, 8012 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 670, 1229, 8012 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 670, 1229, 8012 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 670, 1229, 8012 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 670, 1229, 8012 is 1.
HCF(670, 1229, 8012) = 1
HCF of 670, 1229, 8012 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 670, 1229, 8012 is 1.
Highest Common Factor of 670,1229,8012 is 1
Step 1: Since 1229 > 670, we apply the division lemma to 1229 and 670, to get
1229 = 670 x 1 + 559
Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 559 and 670, to get
670 = 559 x 1 + 111
Step 3: We consider the new divisor 559 and the new remainder 111, and apply the division lemma to get
559 = 111 x 5 + 4
We consider the new divisor 111 and the new remainder 4,and apply the division lemma to get
111 = 4 x 27 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 670 and 1229 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(111,4) = HCF(559,111) = HCF(670,559) = HCF(1229,670) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8012 > 1, we apply the division lemma to 8012 and 1, to get
8012 = 1 x 8012 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8012 is 1
Notice that 1 = HCF(8012,1) .
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Frequently Asked Questions on HCF of 670, 1229, 8012 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 670, 1229, 8012?
Answer: HCF of 670, 1229, 8012 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 670, 1229, 8012 using Euclid's Algorithm?
Answer: For arbitrary numbers 670, 1229, 8012 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
