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 432, 7721 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 432, 7721 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 432, 7721 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 432, 7721 is 1.
HCF(432, 7721) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 432, 7721 is 1.
Step 1: Since 7721 > 432, we apply the division lemma to 7721 and 432, to get
7721 = 432 x 17 + 377
Step 2: Since the reminder 432 ≠ 0, we apply division lemma to 377 and 432, to get
432 = 377 x 1 + 55
Step 3: We consider the new divisor 377 and the new remainder 55, and apply the division lemma to get
377 = 55 x 6 + 47
We consider the new divisor 55 and the new remainder 47,and apply the division lemma to get
55 = 47 x 1 + 8
We consider the new divisor 47 and the new remainder 8,and apply the division lemma to get
47 = 8 x 5 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 432 and 7721 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(47,8) = HCF(55,47) = HCF(377,55) = HCF(432,377) = HCF(7721,432) .
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 432, 7721?
Answer: HCF of 432, 7721 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 432, 7721 using Euclid's Algorithm?
Answer: For arbitrary numbers 432, 7721 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.