Highest Common Factor of 469, 714, 362 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 469, 714, 362 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 469, 714, 362 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 469, 714, 362 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 469, 714, 362 is 1.
HCF(469, 714, 362) = 1
HCF of 469, 714, 362 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 469, 714, 362 is 1.
Highest Common Factor of 469,714,362 is 1
Step 1: Since 714 > 469, we apply the division lemma to 714 and 469, to get
714 = 469 x 1 + 245
Step 2: Since the reminder 469 ≠ 0, we apply division lemma to 245 and 469, to get
469 = 245 x 1 + 224
Step 3: We consider the new divisor 245 and the new remainder 224, and apply the division lemma to get
245 = 224 x 1 + 21
We consider the new divisor 224 and the new remainder 21,and apply the division lemma to get
224 = 21 x 10 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 469 and 714 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(224,21) = HCF(245,224) = HCF(469,245) = HCF(714,469) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 362 > 7, we apply the division lemma to 362 and 7, to get
362 = 7 x 51 + 5
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 5 and 7, to get
7 = 5 x 1 + 2
Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 7 and 362 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(362,7) .
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Frequently Asked Questions on HCF of 469, 714, 362 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 469, 714, 362?
Answer: HCF of 469, 714, 362 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 469, 714, 362 using Euclid's Algorithm?
Answer: For arbitrary numbers 469, 714, 362 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.