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, 690, 377 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 267, 690, 377 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, 690, 377 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, 690, 377 is 1.
HCF(267, 690, 377) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 267, 690, 377 is 1.
Step 1: Since 690 > 267, we apply the division lemma to 690 and 267, to get
690 = 267 x 2 + 156
Step 2: Since the reminder 267 ≠ 0, we apply division lemma to 156 and 267, to get
267 = 156 x 1 + 111
Step 3: We consider the new divisor 156 and the new remainder 111, and apply the division lemma to get
156 = 111 x 1 + 45
We consider the new divisor 111 and the new remainder 45,and apply the division lemma to get
111 = 45 x 2 + 21
We consider the new divisor 45 and the new remainder 21,and apply the division lemma to get
45 = 21 x 2 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 267 and 690 is 3
Notice that 3 = HCF(21,3) = HCF(45,21) = HCF(111,45) = HCF(156,111) = HCF(267,156) = HCF(690,267) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 377 > 3, we apply the division lemma to 377 and 3, to get
377 = 3 x 125 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 377 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(377,3) .
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, 690, 377?
Answer: HCF of 267, 690, 377 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 267, 690, 377 using Euclid's Algorithm?
Answer: For arbitrary numbers 267, 690, 377 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.