Highest Common Factor of 768, 270 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 768, 270 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 270 is 6 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 768, 270 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 768, 270 is 6.
HCF(768, 270) = 6
HCF of 768, 270 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 768, 270 is 6.
Highest Common Factor of 768,270 is 6
Step 1: Since 768 > 270, we apply the division lemma to 768 and 270, to get
768 = 270 x 2 + 228
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 228 and 270, to get
270 = 228 x 1 + 42
Step 3: We consider the new divisor 228 and the new remainder 42, and apply the division lemma to get
228 = 42 x 5 + 18
We consider the new divisor 42 and the new remainder 18,and apply the division lemma to get
42 = 18 x 2 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 768 and 270 is 6
Notice that 6 = HCF(18,6) = HCF(42,18) = HCF(228,42) = HCF(270,228) = HCF(768,270) .
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Frequently Asked Questions on HCF of 768, 270 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 768, 270?
Answer: HCF of 768, 270 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 270 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.