Highest Common Factor of 356, 20610 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 356, 20610 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 356, 20610 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 356, 20610 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 356, 20610 is 2.
HCF(356, 20610) = 2
HCF of 356, 20610 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 356, 20610 is 2.
Highest Common Factor of 356,20610 is 2
Step 1: Since 20610 > 356, we apply the division lemma to 20610 and 356, to get
20610 = 356 x 57 + 318
Step 2: Since the reminder 356 ≠ 0, we apply division lemma to 318 and 356, to get
356 = 318 x 1 + 38
Step 3: We consider the new divisor 318 and the new remainder 38, and apply the division lemma to get
318 = 38 x 8 + 14
We consider the new divisor 38 and the new remainder 14,and apply the division lemma to get
38 = 14 x 2 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 356 and 20610 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(38,14) = HCF(318,38) = HCF(356,318) = HCF(20610,356) .
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Frequently Asked Questions on HCF of 356, 20610 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 356, 20610?
Answer: HCF of 356, 20610 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 356, 20610 using Euclid's Algorithm?
Answer: For arbitrary numbers 356, 20610 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.