Highest Common Factor of 606, 714 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 606, 714 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 606, 714 is 6 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 606, 714 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 606, 714 is 6.
HCF(606, 714) = 6
HCF of 606, 714 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 606, 714 is 6.
Highest Common Factor of 606,714 is 6
Step 1: Since 714 > 606, we apply the division lemma to 714 and 606, to get
714 = 606 x 1 + 108
Step 2: Since the reminder 606 ≠ 0, we apply division lemma to 108 and 606, to get
606 = 108 x 5 + 66
Step 3: We consider the new divisor 108 and the new remainder 66, and apply the division lemma to get
108 = 66 x 1 + 42
We consider the new divisor 66 and the new remainder 42,and apply the division lemma to get
66 = 42 x 1 + 24
We consider the new divisor 42 and the new remainder 24,and apply the division lemma to get
42 = 24 x 1 + 18
We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get
24 = 18 x 1 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 606 and 714 is 6
Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(42,24) = HCF(66,42) = HCF(108,66) = HCF(606,108) = HCF(714,606) .
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Frequently Asked Questions on HCF of 606, 714 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 606, 714?
Answer: HCF of 606, 714 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 606, 714 using Euclid's Algorithm?
Answer: For arbitrary numbers 606, 714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.