Highest Common Factor of 363, 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 363, 506 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 363, 506 is 11 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 363, 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 363, 506 is 11.
HCF(363, 506) = 11
HCF of 363, 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 363, 506 is 11.
Highest Common Factor of 363,506 is 11
Step 1: Since 506 > 363, we apply the division lemma to 506 and 363, to get
506 = 363 x 1 + 143
Step 2: Since the reminder 363 ≠ 0, we apply division lemma to 143 and 363, to get
363 = 143 x 2 + 77
Step 3: We consider the new divisor 143 and the new remainder 77, and apply the division lemma to get
143 = 77 x 1 + 66
We consider the new divisor 77 and the new remainder 66,and apply the division lemma to get
77 = 66 x 1 + 11
We consider the new divisor 66 and the new remainder 11,and apply the division lemma to get
66 = 11 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 363 and 506 is 11
Notice that 11 = HCF(66,11) = HCF(77,66) = HCF(143,77) = HCF(363,143) = HCF(506,363) .
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Frequently Asked Questions on HCF of 363, 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 363, 506?
Answer: HCF of 363, 506 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 363, 506 using Euclid's Algorithm?
Answer: For arbitrary numbers 363, 506 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.