Highest Common Factor of 400, 618, 661 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, 618, 661 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 400, 618, 661 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, 618, 661 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, 618, 661 is 1.
HCF(400, 618, 661) = 1
HCF of 400, 618, 661 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, 618, 661 is 1.
Highest Common Factor of 400,618,661 is 1
Step 1: Since 618 > 400, we apply the division lemma to 618 and 400, to get
618 = 400 x 1 + 218
Step 2: Since the reminder 400 ≠ 0, we apply division lemma to 218 and 400, to get
400 = 218 x 1 + 182
Step 3: We consider the new divisor 218 and the new remainder 182, and apply the division lemma to get
218 = 182 x 1 + 36
We consider the new divisor 182 and the new remainder 36,and apply the division lemma to get
182 = 36 x 5 + 2
We consider the new divisor 36 and the new remainder 2,and apply the division lemma to get
36 = 2 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 400 and 618 is 2
Notice that 2 = HCF(36,2) = HCF(182,36) = HCF(218,182) = HCF(400,218) = HCF(618,400) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 661 > 2, we apply the division lemma to 661 and 2, to get
661 = 2 x 330 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 661 is 1
Notice that 1 = HCF(2,1) = HCF(661,2) .
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Frequently Asked Questions on HCF of 400, 618, 661 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, 618, 661?
Answer: HCF of 400, 618, 661 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 400, 618, 661 using Euclid's Algorithm?
Answer: For arbitrary numbers 400, 618, 661 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.