Highest Common Factor of 400, 609 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 400, 609 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 400, 609 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 400, 609 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 400, 609 is 1.
HCF(400, 609) = 1
HCF of 400, 609 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 400, 609 is 1.
Highest Common Factor of 400,609 is 1
Step 1: Since 609 > 400, we apply the division lemma to 609 and 400, to get
609 = 400 x 1 + 209
Step 2: Since the reminder 400 ≠ 0, we apply division lemma to 209 and 400, to get
400 = 209 x 1 + 191
Step 3: We consider the new divisor 209 and the new remainder 191, and apply the division lemma to get
209 = 191 x 1 + 18
We consider the new divisor 191 and the new remainder 18,and apply the division lemma to get
191 = 18 x 10 + 11
We consider the new divisor 18 and the new remainder 11,and apply the division lemma to get
18 = 11 x 1 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 400 and 609 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(191,18) = HCF(209,191) = HCF(400,209) = HCF(609,400) .
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Frequently Asked Questions on HCF of 400, 609 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 400, 609?
Answer: HCF of 400, 609 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 400, 609 using Euclid's Algorithm?
Answer: For arbitrary numbers 400, 609 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.