Highest Common Factor of 972, 706, 433 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 972, 706, 433 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 706, 433 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 972, 706, 433 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 972, 706, 433 is 1.
HCF(972, 706, 433) = 1
HCF of 972, 706, 433 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 706, 433 is 1.
Highest Common Factor of 972,706,433 is 1
Step 1: Since 972 > 706, we apply the division lemma to 972 and 706, to get
972 = 706 x 1 + 266
Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 266 and 706, to get
706 = 266 x 2 + 174
Step 3: We consider the new divisor 266 and the new remainder 174, and apply the division lemma to get
266 = 174 x 1 + 92
We consider the new divisor 174 and the new remainder 92,and apply the division lemma to get
174 = 92 x 1 + 82
We consider the new divisor 92 and the new remainder 82,and apply the division lemma to get
92 = 82 x 1 + 10
We consider the new divisor 82 and the new remainder 10,and apply the division lemma to get
82 = 10 x 8 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 972 and 706 is 2
Notice that 2 = HCF(10,2) = HCF(82,10) = HCF(92,82) = HCF(174,92) = HCF(266,174) = HCF(706,266) = HCF(972,706) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 433 > 2, we apply the division lemma to 433 and 2, to get
433 = 2 x 216 + 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 433 is 1
Notice that 1 = HCF(2,1) = HCF(433,2) .
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Frequently Asked Questions on HCF of 972, 706, 433 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 972, 706, 433?
Answer: HCF of 972, 706, 433 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 706, 433 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 706, 433 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.