Highest Common Factor of 696, 37654 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 696, 37654 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 696, 37654 is 2 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 696, 37654 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 696, 37654 is 2.
HCF(696, 37654) = 2
HCF of 696, 37654 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 696, 37654 is 2.
Highest Common Factor of 696,37654 is 2
Step 1: Since 37654 > 696, we apply the division lemma to 37654 and 696, to get
37654 = 696 x 54 + 70
Step 2: Since the reminder 696 ≠ 0, we apply division lemma to 70 and 696, to get
696 = 70 x 9 + 66
Step 3: We consider the new divisor 70 and the new remainder 66, and apply the division lemma to get
70 = 66 x 1 + 4
We consider the new divisor 66 and the new remainder 4,and apply the division lemma to get
66 = 4 x 16 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 696 and 37654 is 2
Notice that 2 = HCF(4,2) = HCF(66,4) = HCF(70,66) = HCF(696,70) = HCF(37654,696) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 696, 37654 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 696, 37654?
Answer: HCF of 696, 37654 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 696, 37654 using Euclid's Algorithm?
Answer: For arbitrary numbers 696, 37654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.