Highest Common Factor of 270, 693 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 270, 693 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 270, 693 is 9 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 270, 693 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 270, 693 is 9.
HCF(270, 693) = 9
HCF of 270, 693 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 270, 693 is 9.
Highest Common Factor of 270,693 is 9
Step 1: Since 693 > 270, we apply the division lemma to 693 and 270, to get
693 = 270 x 2 + 153
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 153 and 270, to get
270 = 153 x 1 + 117
Step 3: We consider the new divisor 153 and the new remainder 117, and apply the division lemma to get
153 = 117 x 1 + 36
We consider the new divisor 117 and the new remainder 36,and apply the division lemma to get
117 = 36 x 3 + 9
We consider the new divisor 36 and the new remainder 9,and apply the division lemma to get
36 = 9 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 270 and 693 is 9
Notice that 9 = HCF(36,9) = HCF(117,36) = HCF(153,117) = HCF(270,153) = HCF(693,270) .
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Frequently Asked Questions on HCF of 270, 693 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 270, 693?
Answer: HCF of 270, 693 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 270, 693 using Euclid's Algorithm?
Answer: For arbitrary numbers 270, 693 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.