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 524, 716, 267 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 524, 716, 267 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 524, 716, 267 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 524, 716, 267 is 1.
HCF(524, 716, 267) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 524, 716, 267 is 1.
Step 1: Since 716 > 524, we apply the division lemma to 716 and 524, to get
716 = 524 x 1 + 192
Step 2: Since the reminder 524 ≠ 0, we apply division lemma to 192 and 524, to get
524 = 192 x 2 + 140
Step 3: We consider the new divisor 192 and the new remainder 140, and apply the division lemma to get
192 = 140 x 1 + 52
We consider the new divisor 140 and the new remainder 52,and apply the division lemma to get
140 = 52 x 2 + 36
We consider the new divisor 52 and the new remainder 36,and apply the division lemma to get
52 = 36 x 1 + 16
We consider the new divisor 36 and the new remainder 16,and apply the division lemma to get
36 = 16 x 2 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 524 and 716 is 4
Notice that 4 = HCF(16,4) = HCF(36,16) = HCF(52,36) = HCF(140,52) = HCF(192,140) = HCF(524,192) = HCF(716,524) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 267 > 4, we apply the division lemma to 267 and 4, to get
267 = 4 x 66 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma 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 4 and 267 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(267,4) .
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 524, 716, 267?
Answer: HCF of 524, 716, 267 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 524, 716, 267 using Euclid's Algorithm?
Answer: For arbitrary numbers 524, 716, 267 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.