Highest Common Factor of 423, 669, 106, 74 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 423, 669, 106, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 423, 669, 106, 74 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 423, 669, 106, 74 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 423, 669, 106, 74 is 1.
HCF(423, 669, 106, 74) = 1
HCF of 423, 669, 106, 74 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 423, 669, 106, 74 is 1.
Highest Common Factor of 423,669,106,74 is 1
Step 1: Since 669 > 423, we apply the division lemma to 669 and 423, to get
669 = 423 x 1 + 246
Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 246 and 423, to get
423 = 246 x 1 + 177
Step 3: We consider the new divisor 246 and the new remainder 177, and apply the division lemma to get
246 = 177 x 1 + 69
We consider the new divisor 177 and the new remainder 69,and apply the division lemma to get
177 = 69 x 2 + 39
We consider the new divisor 69 and the new remainder 39,and apply the division lemma to get
69 = 39 x 1 + 30
We consider the new divisor 39 and the new remainder 30,and apply the division lemma to get
39 = 30 x 1 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 423 and 669 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(39,30) = HCF(69,39) = HCF(177,69) = HCF(246,177) = HCF(423,246) = HCF(669,423) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 106 > 3, we apply the division lemma to 106 and 3, to get
106 = 3 x 35 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 106 is 1
Notice that 1 = HCF(3,1) = HCF(106,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 1, we apply the division lemma to 74 and 1, to get
74 = 1 x 74 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74 is 1
Notice that 1 = HCF(74,1) .
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Frequently Asked Questions on HCF of 423, 669, 106, 74 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 423, 669, 106, 74?
Answer: HCF of 423, 669, 106, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 423, 669, 106, 74 using Euclid's Algorithm?
Answer: For arbitrary numbers 423, 669, 106, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.