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 267, 402, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 267, 402, 691 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 267, 402, 691 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 267, 402, 691 is 1.
HCF(267, 402, 691) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 267, 402, 691 is 1.
Step 1: Since 402 > 267, we apply the division lemma to 402 and 267, to get
402 = 267 x 1 + 135
Step 2: Since the reminder 267 ≠ 0, we apply division lemma to 135 and 267, to get
267 = 135 x 1 + 132
Step 3: We consider the new divisor 135 and the new remainder 132, and apply the division lemma to get
135 = 132 x 1 + 3
We consider the new divisor 132 and the new remainder 3, and apply the division lemma to get
132 = 3 x 44 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 267 and 402 is 3
Notice that 3 = HCF(132,3) = HCF(135,132) = HCF(267,135) = HCF(402,267) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 691 > 3, we apply the division lemma to 691 and 3, to get
691 = 3 x 230 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 691 is 1
Notice that 1 = HCF(3,1) = HCF(691,3) .
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 267, 402, 691?
Answer: HCF of 267, 402, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 267, 402, 691 using Euclid's Algorithm?
Answer: For arbitrary numbers 267, 402, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.