Highest Common Factor of 672, 364, 406 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 672, 364, 406 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 672, 364, 406 is 14 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 672, 364, 406 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 672, 364, 406 is 14.
HCF(672, 364, 406) = 14
HCF of 672, 364, 406 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 672, 364, 406 is 14.
Highest Common Factor of 672,364,406 is 14
Step 1: Since 672 > 364, we apply the division lemma to 672 and 364, to get
672 = 364 x 1 + 308
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 308 and 364, to get
364 = 308 x 1 + 56
Step 3: We consider the new divisor 308 and the new remainder 56, and apply the division lemma to get
308 = 56 x 5 + 28
We consider the new divisor 56 and the new remainder 28, and apply the division lemma to get
56 = 28 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 672 and 364 is 28
Notice that 28 = HCF(56,28) = HCF(308,56) = HCF(364,308) = HCF(672,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 406 > 28, we apply the division lemma to 406 and 28, to get
406 = 28 x 14 + 14
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 14 and 28, to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 28 and 406 is 14
Notice that 14 = HCF(28,14) = HCF(406,28) .
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Frequently Asked Questions on HCF of 672, 364, 406 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 672, 364, 406?
Answer: HCF of 672, 364, 406 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 672, 364, 406 using Euclid's Algorithm?
Answer: For arbitrary numbers 672, 364, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
