Highest Common Factor of 630, 888, 689 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 630, 888, 689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 630, 888, 689 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 630, 888, 689 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 630, 888, 689 is 1.
HCF(630, 888, 689) = 1
HCF of 630, 888, 689 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 630, 888, 689 is 1.
Highest Common Factor of 630,888,689 is 1
Step 1: Since 888 > 630, we apply the division lemma to 888 and 630, to get
888 = 630 x 1 + 258
Step 2: Since the reminder 630 ≠ 0, we apply division lemma to 258 and 630, to get
630 = 258 x 2 + 114
Step 3: We consider the new divisor 258 and the new remainder 114, and apply the division lemma to get
258 = 114 x 2 + 30
We consider the new divisor 114 and the new remainder 30,and apply the division lemma to get
114 = 30 x 3 + 24
We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 630 and 888 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(114,30) = HCF(258,114) = HCF(630,258) = HCF(888,630) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 689 > 6, we apply the division lemma to 689 and 6, to get
689 = 6 x 114 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 689 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(689,6) .
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Frequently Asked Questions on HCF of 630, 888, 689 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 630, 888, 689?
Answer: HCF of 630, 888, 689 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 630, 888, 689 using Euclid's Algorithm?
Answer: For arbitrary numbers 630, 888, 689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.