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 692, 431, 775 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 692, 431, 775 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 692, 431, 775 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 692, 431, 775 is 1.
HCF(692, 431, 775) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 692, 431, 775 is 1.
Step 1: Since 692 > 431, we apply the division lemma to 692 and 431, to get
692 = 431 x 1 + 261
Step 2: Since the reminder 431 ≠ 0, we apply division lemma to 261 and 431, to get
431 = 261 x 1 + 170
Step 3: We consider the new divisor 261 and the new remainder 170, and apply the division lemma to get
261 = 170 x 1 + 91
We consider the new divisor 170 and the new remainder 91,and apply the division lemma to get
170 = 91 x 1 + 79
We consider the new divisor 91 and the new remainder 79,and apply the division lemma to get
91 = 79 x 1 + 12
We consider the new divisor 79 and the new remainder 12,and apply the division lemma to get
79 = 12 x 6 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 692 and 431 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(79,12) = HCF(91,79) = HCF(170,91) = HCF(261,170) = HCF(431,261) = HCF(692,431) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 775 > 1, we apply the division lemma to 775 and 1, to get
775 = 1 x 775 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 775 is 1
Notice that 1 = HCF(775,1) .
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 692, 431, 775?
Answer: HCF of 692, 431, 775 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 692, 431, 775 using Euclid's Algorithm?
Answer: For arbitrary numbers 692, 431, 775 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.