Highest Common Factor of 768, 135 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, 135 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 135 is 3 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, 135 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, 135 is 3.
HCF(768, 135) = 3
HCF of 768, 135 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, 135 is 3.
Highest Common Factor of 768,135 is 3
Step 1: Since 768 > 135, we apply the division lemma to 768 and 135, to get
768 = 135 x 5 + 93
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 93 and 135, to get
135 = 93 x 1 + 42
Step 3: We consider the new divisor 93 and the new remainder 42, and apply the division lemma to get
93 = 42 x 2 + 9
We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get
42 = 9 x 4 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 768 and 135 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(93,42) = HCF(135,93) = HCF(768,135) .
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Frequently Asked Questions on HCF of 768, 135 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, 135?
Answer: HCF of 768, 135 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 135 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.