Highest Common Factor of 659, 33969 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 659, 33969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 659, 33969 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 659, 33969 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 659, 33969 is 1.
HCF(659, 33969) = 1
HCF of 659, 33969 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 659, 33969 is 1.
Highest Common Factor of 659,33969 is 1
Step 1: Since 33969 > 659, we apply the division lemma to 33969 and 659, to get
33969 = 659 x 51 + 360
Step 2: Since the reminder 659 ≠ 0, we apply division lemma to 360 and 659, to get
659 = 360 x 1 + 299
Step 3: We consider the new divisor 360 and the new remainder 299, and apply the division lemma to get
360 = 299 x 1 + 61
We consider the new divisor 299 and the new remainder 61,and apply the division lemma to get
299 = 61 x 4 + 55
We consider the new divisor 61 and the new remainder 55,and apply the division lemma to get
61 = 55 x 1 + 6
We consider the new divisor 55 and the new remainder 6,and apply the division lemma to get
55 = 6 x 9 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 659 and 33969 is 1
Notice that 1 = HCF(6,1) = HCF(55,6) = HCF(61,55) = HCF(299,61) = HCF(360,299) = HCF(659,360) = HCF(33969,659) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 659, 33969 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 659, 33969?
Answer: HCF of 659, 33969 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 659, 33969 using Euclid's Algorithm?
Answer: For arbitrary numbers 659, 33969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.