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 764, 302, 83 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 764, 302, 83 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 764, 302, 83 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 764, 302, 83 is 1.
HCF(764, 302, 83) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 764, 302, 83 is 1.
Step 1: Since 764 > 302, we apply the division lemma to 764 and 302, to get
764 = 302 x 2 + 160
Step 2: Since the reminder 302 ≠ 0, we apply division lemma to 160 and 302, to get
302 = 160 x 1 + 142
Step 3: We consider the new divisor 160 and the new remainder 142, and apply the division lemma to get
160 = 142 x 1 + 18
We consider the new divisor 142 and the new remainder 18,and apply the division lemma to get
142 = 18 x 7 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 764 and 302 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(142,18) = HCF(160,142) = HCF(302,160) = HCF(764,302) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 83 > 2, we apply the division lemma to 83 and 2, to get
83 = 2 x 41 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 83 is 1
Notice that 1 = HCF(2,1) = HCF(83,2) .
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 764, 302, 83?
Answer: HCF of 764, 302, 83 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 764, 302, 83 using Euclid's Algorithm?
Answer: For arbitrary numbers 764, 302, 83 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.