Highest Common Factor of 408, 670 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 408, 670 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 670 is 2 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 408, 670 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 408, 670 is 2.
HCF(408, 670) = 2
HCF of 408, 670 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 408, 670 is 2.
Highest Common Factor of 408,670 is 2
Step 1: Since 670 > 408, we apply the division lemma to 670 and 408, to get
670 = 408 x 1 + 262
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 262 and 408, to get
408 = 262 x 1 + 146
Step 3: We consider the new divisor 262 and the new remainder 146, and apply the division lemma to get
262 = 146 x 1 + 116
We consider the new divisor 146 and the new remainder 116,and apply the division lemma to get
146 = 116 x 1 + 30
We consider the new divisor 116 and the new remainder 30,and apply the division lemma to get
116 = 30 x 3 + 26
We consider the new divisor 30 and the new remainder 26,and apply the division lemma to get
30 = 26 x 1 + 4
We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get
26 = 4 x 6 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 408 and 670 is 2
Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(30,26) = HCF(116,30) = HCF(146,116) = HCF(262,146) = HCF(408,262) = HCF(670,408) .
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Frequently Asked Questions on HCF of 408, 670 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 408, 670?
Answer: HCF of 408, 670 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 670 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.