Highest Common Factor of 189, 693, 70 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 189, 693, 70 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 189, 693, 70 is 7 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 189, 693, 70 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 189, 693, 70 is 7.
HCF(189, 693, 70) = 7
HCF of 189, 693, 70 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 189, 693, 70 is 7.
Highest Common Factor of 189,693,70 is 7
Step 1: Since 693 > 189, we apply the division lemma to 693 and 189, to get
693 = 189 x 3 + 126
Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 126 and 189, to get
189 = 126 x 1 + 63
Step 3: We consider the new divisor 126 and the new remainder 63, and apply the division lemma to get
126 = 63 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 63, the HCF of 189 and 693 is 63
Notice that 63 = HCF(126,63) = HCF(189,126) = HCF(693,189) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 70 > 63, we apply the division lemma to 70 and 63, to get
70 = 63 x 1 + 7
Step 2: Since the reminder 63 ≠ 0, we apply division lemma to 7 and 63, to get
63 = 7 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 63 and 70 is 7
Notice that 7 = HCF(63,7) = HCF(70,63) .
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Frequently Asked Questions on HCF of 189, 693, 70 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 189, 693, 70?
Answer: HCF of 189, 693, 70 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 189, 693, 70 using Euclid's Algorithm?
Answer: For arbitrary numbers 189, 693, 70 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.