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 765, 933, 106 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 765, 933, 106 is 1 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 765, 933, 106 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 765, 933, 106 is 1.
HCF(765, 933, 106) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 765, 933, 106 is 1.
Step 1: Since 933 > 765, we apply the division lemma to 933 and 765, to get
933 = 765 x 1 + 168
Step 2: Since the reminder 765 ≠ 0, we apply division lemma to 168 and 765, to get
765 = 168 x 4 + 93
Step 3: We consider the new divisor 168 and the new remainder 93, and apply the division lemma to get
168 = 93 x 1 + 75
We consider the new divisor 93 and the new remainder 75,and apply the division lemma to get
93 = 75 x 1 + 18
We consider the new divisor 75 and the new remainder 18,and apply the division lemma to get
75 = 18 x 4 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 765 and 933 is 3
Notice that 3 = HCF(18,3) = HCF(75,18) = HCF(93,75) = HCF(168,93) = HCF(765,168) = HCF(933,765) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 106 > 3, we apply the division lemma to 106 and 3, to get
106 = 3 x 35 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 106 is 1
Notice that 1 = HCF(3,1) = HCF(106,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 765, 933, 106?
Answer: HCF of 765, 933, 106 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 765, 933, 106 using Euclid's Algorithm?
Answer: For arbitrary numbers 765, 933, 106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.