Highest Common Factor of 362, 506 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 362, 506 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 362, 506 is 2 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 362, 506 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 362, 506 is 2.
HCF(362, 506) = 2
HCF of 362, 506 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 362, 506 is 2.
Highest Common Factor of 362,506 is 2
Step 1: Since 506 > 362, we apply the division lemma to 506 and 362, to get
506 = 362 x 1 + 144
Step 2: Since the reminder 362 ≠ 0, we apply division lemma to 144 and 362, to get
362 = 144 x 2 + 74
Step 3: We consider the new divisor 144 and the new remainder 74, and apply the division lemma to get
144 = 74 x 1 + 70
We consider the new divisor 74 and the new remainder 70,and apply the division lemma to get
74 = 70 x 1 + 4
We consider the new divisor 70 and the new remainder 4,and apply the division lemma to get
70 = 4 x 17 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 362 and 506 is 2
Notice that 2 = HCF(4,2) = HCF(70,4) = HCF(74,70) = HCF(144,74) = HCF(362,144) = HCF(506,362) .
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Frequently Asked Questions on HCF of 362, 506 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 362, 506?
Answer: HCF of 362, 506 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 362, 506 using Euclid's Algorithm?
Answer: For arbitrary numbers 362, 506 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.