Highest Common Factor of 685, 972, 16 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 685, 972, 16 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 685, 972, 16 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 685, 972, 16 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 685, 972, 16 is 1.
HCF(685, 972, 16) = 1
HCF of 685, 972, 16 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 685, 972, 16 is 1.
Highest Common Factor of 685,972,16 is 1
Step 1: Since 972 > 685, we apply the division lemma to 972 and 685, to get
972 = 685 x 1 + 287
Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 287 and 685, to get
685 = 287 x 2 + 111
Step 3: We consider the new divisor 287 and the new remainder 111, and apply the division lemma to get
287 = 111 x 2 + 65
We consider the new divisor 111 and the new remainder 65,and apply the division lemma to get
111 = 65 x 1 + 46
We consider the new divisor 65 and the new remainder 46,and apply the division lemma to get
65 = 46 x 1 + 19
We consider the new divisor 46 and the new remainder 19,and apply the division lemma to get
46 = 19 x 2 + 8
We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get
19 = 8 x 2 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 685 and 972 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(46,19) = HCF(65,46) = HCF(111,65) = HCF(287,111) = HCF(685,287) = HCF(972,685) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 1, we apply the division lemma to 16 and 1, to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 16 is 1
Notice that 1 = HCF(16,1) .
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Frequently Asked Questions on HCF of 685, 972, 16 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 685, 972, 16?
Answer: HCF of 685, 972, 16 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 685, 972, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 685, 972, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.