Highest Common Factor of 661, 3688, 4998 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 661, 3688, 4998 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 661, 3688, 4998 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 661, 3688, 4998 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 661, 3688, 4998 is 1.
HCF(661, 3688, 4998) = 1
HCF of 661, 3688, 4998 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 661, 3688, 4998 is 1.
Highest Common Factor of 661,3688,4998 is 1
Step 1: Since 3688 > 661, we apply the division lemma to 3688 and 661, to get
3688 = 661 x 5 + 383
Step 2: Since the reminder 661 ≠ 0, we apply division lemma to 383 and 661, to get
661 = 383 x 1 + 278
Step 3: We consider the new divisor 383 and the new remainder 278, and apply the division lemma to get
383 = 278 x 1 + 105
We consider the new divisor 278 and the new remainder 105,and apply the division lemma to get
278 = 105 x 2 + 68
We consider the new divisor 105 and the new remainder 68,and apply the division lemma to get
105 = 68 x 1 + 37
We consider the new divisor 68 and the new remainder 37,and apply the division lemma to get
68 = 37 x 1 + 31
We consider the new divisor 37 and the new remainder 31,and apply the division lemma to get
37 = 31 x 1 + 6
We consider the new divisor 31 and the new remainder 6,and apply the division lemma to get
31 = 6 x 5 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 661 and 3688 is 1
Notice that 1 = HCF(6,1) = HCF(31,6) = HCF(37,31) = HCF(68,37) = HCF(105,68) = HCF(278,105) = HCF(383,278) = HCF(661,383) = HCF(3688,661) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4998 > 1, we apply the division lemma to 4998 and 1, to get
4998 = 1 x 4998 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 4998 is 1
Notice that 1 = HCF(4998,1) .
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Frequently Asked Questions on HCF of 661, 3688, 4998 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 661, 3688, 4998?
Answer: HCF of 661, 3688, 4998 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 661, 3688, 4998 using Euclid's Algorithm?
Answer: For arbitrary numbers 661, 3688, 4998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.