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 431, 966, 698 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 431, 966, 698 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 431, 966, 698 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 431, 966, 698 is 1.
HCF(431, 966, 698) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 431, 966, 698 is 1.
Step 1: Since 966 > 431, we apply the division lemma to 966 and 431, to get
966 = 431 x 2 + 104
Step 2: Since the reminder 431 ≠ 0, we apply division lemma to 104 and 431, to get
431 = 104 x 4 + 15
Step 3: We consider the new divisor 104 and the new remainder 15, and apply the division lemma to get
104 = 15 x 6 + 14
We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get
15 = 14 x 1 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 431 and 966 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(104,15) = HCF(431,104) = HCF(966,431) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 698 > 1, we apply the division lemma to 698 and 1, to get
698 = 1 x 698 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 698 is 1
Notice that 1 = HCF(698,1) .
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 431, 966, 698?
Answer: HCF of 431, 966, 698 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 431, 966, 698 using Euclid's Algorithm?
Answer: For arbitrary numbers 431, 966, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.