Highest Common Factor of 693, 945, 229 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 693, 945, 229 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 693, 945, 229 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 693, 945, 229 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 693, 945, 229 is 1.
HCF(693, 945, 229) = 1
HCF of 693, 945, 229 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 693, 945, 229 is 1.
Highest Common Factor of 693,945,229 is 1
Step 1: Since 945 > 693, we apply the division lemma to 945 and 693, to get
945 = 693 x 1 + 252
Step 2: Since the reminder 693 ≠ 0, we apply division lemma to 252 and 693, to get
693 = 252 x 2 + 189
Step 3: We consider the new divisor 252 and the new remainder 189, and apply the division lemma to get
252 = 189 x 1 + 63
We consider the new divisor 189 and the new remainder 63, and apply the division lemma to get
189 = 63 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 63, the HCF of 693 and 945 is 63
Notice that 63 = HCF(189,63) = HCF(252,189) = HCF(693,252) = HCF(945,693) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 229 > 63, we apply the division lemma to 229 and 63, to get
229 = 63 x 3 + 40
Step 2: Since the reminder 63 ≠ 0, we apply division lemma to 40 and 63, to get
63 = 40 x 1 + 23
Step 3: We consider the new divisor 40 and the new remainder 23, and apply the division lemma to get
40 = 23 x 1 + 17
We consider the new divisor 23 and the new remainder 17,and apply the division lemma to get
23 = 17 x 1 + 6
We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get
17 = 6 x 2 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 63 and 229 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(23,17) = HCF(40,23) = HCF(63,40) = HCF(229,63) .
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Frequently Asked Questions on HCF of 693, 945, 229 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 693, 945, 229?
Answer: HCF of 693, 945, 229 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 693, 945, 229 using Euclid's Algorithm?
Answer: For arbitrary numbers 693, 945, 229 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.