Highest Common Factor of 630, 414, 359 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, 414, 359 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 630, 414, 359 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, 414, 359 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, 414, 359 is 1.
HCF(630, 414, 359) = 1
HCF of 630, 414, 359 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, 414, 359 is 1.
Highest Common Factor of 630,414,359 is 1
Step 1: Since 630 > 414, we apply the division lemma to 630 and 414, to get
630 = 414 x 1 + 216
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 216 and 414, to get
414 = 216 x 1 + 198
Step 3: We consider the new divisor 216 and the new remainder 198, and apply the division lemma to get
216 = 198 x 1 + 18
We consider the new divisor 198 and the new remainder 18, and apply the division lemma to get
198 = 18 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 630 and 414 is 18
Notice that 18 = HCF(198,18) = HCF(216,198) = HCF(414,216) = HCF(630,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 359 > 18, we apply the division lemma to 359 and 18, to get
359 = 18 x 19 + 17
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 17 and 18, to get
18 = 17 x 1 + 1
Step 3: We consider the new divisor 17 and the new remainder 1, and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 18 and 359 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(359,18) .
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Frequently Asked Questions on HCF of 630, 414, 359 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, 414, 359?
Answer: HCF of 630, 414, 359 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 630, 414, 359 using Euclid's Algorithm?
Answer: For arbitrary numbers 630, 414, 359 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.