Highest Common Factor of 630, 138, 969, 418 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, 138, 969, 418 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 630, 138, 969, 418 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, 138, 969, 418 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, 138, 969, 418 is 1.
HCF(630, 138, 969, 418) = 1
HCF of 630, 138, 969, 418 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, 138, 969, 418 is 1.
Highest Common Factor of 630,138,969,418 is 1
Step 1: Since 630 > 138, we apply the division lemma to 630 and 138, to get
630 = 138 x 4 + 78
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 78 and 138, to get
138 = 78 x 1 + 60
Step 3: We consider the new divisor 78 and the new remainder 60, and apply the division lemma to get
78 = 60 x 1 + 18
We consider the new divisor 60 and the new remainder 18,and apply the division lemma to get
60 = 18 x 3 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 630 and 138 is 6
Notice that 6 = HCF(18,6) = HCF(60,18) = HCF(78,60) = HCF(138,78) = HCF(630,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 969 > 6, we apply the division lemma to 969 and 6, to get
969 = 6 x 161 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 969 is 3
Notice that 3 = HCF(6,3) = HCF(969,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 418 > 3, we apply the division lemma to 418 and 3, to get
418 = 3 x 139 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 418 is 1
Notice that 1 = HCF(3,1) = HCF(418,3) .
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Frequently Asked Questions on HCF of 630, 138, 969, 418 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, 138, 969, 418?
Answer: HCF of 630, 138, 969, 418 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 630, 138, 969, 418 using Euclid's Algorithm?
Answer: For arbitrary numbers 630, 138, 969, 418 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.