Highest Common Factor of 702, 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 702, 506 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 702, 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 702, 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 702, 506 is 2.
HCF(702, 506) = 2
HCF of 702, 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 702, 506 is 2.
Highest Common Factor of 702,506 is 2
Step 1: Since 702 > 506, we apply the division lemma to 702 and 506, to get
702 = 506 x 1 + 196
Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 196 and 506, to get
506 = 196 x 2 + 114
Step 3: We consider the new divisor 196 and the new remainder 114, and apply the division lemma to get
196 = 114 x 1 + 82
We consider the new divisor 114 and the new remainder 82,and apply the division lemma to get
114 = 82 x 1 + 32
We consider the new divisor 82 and the new remainder 32,and apply the division lemma to get
82 = 32 x 2 + 18
We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get
32 = 18 x 1 + 14
We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 702 and 506 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(82,32) = HCF(114,82) = HCF(196,114) = HCF(506,196) = HCF(702,506) .
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Frequently Asked Questions on HCF of 702, 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 702, 506?
Answer: HCF of 702, 506 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 702, 506 using Euclid's Algorithm?
Answer: For arbitrary numbers 702, 506 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.