Highest Common Factor of 88, 669, 612 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 88, 669, 612 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 88, 669, 612 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 88, 669, 612 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 88, 669, 612 is 1.
HCF(88, 669, 612) = 1
HCF of 88, 669, 612 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 88, 669, 612 is 1.
Highest Common Factor of 88,669,612 is 1
Step 1: Since 669 > 88, we apply the division lemma to 669 and 88, to get
669 = 88 x 7 + 53
Step 2: Since the reminder 88 ≠ 0, we apply division lemma to 53 and 88, to get
88 = 53 x 1 + 35
Step 3: We consider the new divisor 53 and the new remainder 35, and apply the division lemma to get
53 = 35 x 1 + 18
We consider the new divisor 35 and the new remainder 18,and apply the division lemma to get
35 = 18 x 1 + 17
We consider the new divisor 18 and the new remainder 17,and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 88 and 669 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(35,18) = HCF(53,35) = HCF(88,53) = HCF(669,88) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 612 > 1, we apply the division lemma to 612 and 1, to get
612 = 1 x 612 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 612 is 1
Notice that 1 = HCF(612,1) .
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Frequently Asked Questions on HCF of 88, 669, 612 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 88, 669, 612?
Answer: HCF of 88, 669, 612 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 88, 669, 612 using Euclid's Algorithm?
Answer: For arbitrary numbers 88, 669, 612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.