Highest Common Factor of 423, 672, 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 423, 672, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 423, 672, 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 423, 672, 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 423, 672, 407 is 1.
HCF(423, 672, 407) = 1
HCF of 423, 672, 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 423, 672, 407 is 1.
Highest Common Factor of 423,672,407 is 1
Step 1: Since 672 > 423, we apply the division lemma to 672 and 423, to get
672 = 423 x 1 + 249
Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 249 and 423, to get
423 = 249 x 1 + 174
Step 3: We consider the new divisor 249 and the new remainder 174, and apply the division lemma to get
249 = 174 x 1 + 75
We consider the new divisor 174 and the new remainder 75,and apply the division lemma to get
174 = 75 x 2 + 24
We consider the new divisor 75 and the new remainder 24,and apply the division lemma to get
75 = 24 x 3 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 423 and 672 is 3
Notice that 3 = HCF(24,3) = HCF(75,24) = HCF(174,75) = HCF(249,174) = HCF(423,249) = HCF(672,423) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 407 > 3, we apply the division lemma to 407 and 3, to get
407 = 3 x 135 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 407 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(407,3) .
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Frequently Asked Questions on HCF of 423, 672, 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 423, 672, 407?
Answer: HCF of 423, 672, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 423, 672, 407 using Euclid's Algorithm?
Answer: For arbitrary numbers 423, 672, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.