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 759, 21971 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 759, 21971 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 759, 21971 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 759, 21971 is 1.
HCF(759, 21971) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 759, 21971 is 1.
Step 1: Since 21971 > 759, we apply the division lemma to 21971 and 759, to get
21971 = 759 x 28 + 719
Step 2: Since the reminder 759 ≠ 0, we apply division lemma to 719 and 759, to get
759 = 719 x 1 + 40
Step 3: We consider the new divisor 719 and the new remainder 40, and apply the division lemma to get
719 = 40 x 17 + 39
We consider the new divisor 40 and the new remainder 39,and apply the division lemma to get
40 = 39 x 1 + 1
We consider the new divisor 39 and the new remainder 1,and apply the division lemma to get
39 = 1 x 39 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 759 and 21971 is 1
Notice that 1 = HCF(39,1) = HCF(40,39) = HCF(719,40) = HCF(759,719) = HCF(21971,759) .
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 759, 21971?
Answer: HCF of 759, 21971 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 759, 21971 using Euclid's Algorithm?
Answer: For arbitrary numbers 759, 21971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.