Highest Common Factor of 968, 685 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 968, 685 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 968, 685 is 1 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 968, 685 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 968, 685 is 1.
HCF(968, 685) = 1
HCF of 968, 685 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 968, 685 is 1.
Highest Common Factor of 968,685 is 1
Step 1: Since 968 > 685, we apply the division lemma to 968 and 685, to get
968 = 685 x 1 + 283
Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 283 and 685, to get
685 = 283 x 2 + 119
Step 3: We consider the new divisor 283 and the new remainder 119, and apply the division lemma to get
283 = 119 x 2 + 45
We consider the new divisor 119 and the new remainder 45,and apply the division lemma to get
119 = 45 x 2 + 29
We consider the new divisor 45 and the new remainder 29,and apply the division lemma to get
45 = 29 x 1 + 16
We consider the new divisor 29 and the new remainder 16,and apply the division lemma to get
29 = 16 x 1 + 13
We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get
16 = 13 x 1 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 968 and 685 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(29,16) = HCF(45,29) = HCF(119,45) = HCF(283,119) = HCF(685,283) = HCF(968,685) .
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Frequently Asked Questions on HCF of 968, 685 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 968, 685?
Answer: HCF of 968, 685 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 968, 685 using Euclid's Algorithm?
Answer: For arbitrary numbers 968, 685 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.