Highest Common Factor of 135, 765, 699 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 135, 765, 699 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 135, 765, 699 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 135, 765, 699 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 135, 765, 699 is 3.
HCF(135, 765, 699) = 3
HCF of 135, 765, 699 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 135, 765, 699 is 3.
Highest Common Factor of 135,765,699 is 3
Step 1: Since 765 > 135, we apply the division lemma to 765 and 135, to get
765 = 135 x 5 + 90
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 90 and 135, to get
135 = 90 x 1 + 45
Step 3: We consider the new divisor 90 and the new remainder 45, and apply the division lemma to get
90 = 45 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 135 and 765 is 45
Notice that 45 = HCF(90,45) = HCF(135,90) = HCF(765,135) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 699 > 45, we apply the division lemma to 699 and 45, to get
699 = 45 x 15 + 24
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 24 and 45, to get
45 = 24 x 1 + 21
Step 3: We consider the new divisor 24 and the new remainder 21, and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3, and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 45 and 699 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(699,45) .
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Frequently Asked Questions on HCF of 135, 765, 699 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 135, 765, 699?
Answer: HCF of 135, 765, 699 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 135, 765, 699 using Euclid's Algorithm?
Answer: For arbitrary numbers 135, 765, 699 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.