Highest Common Factor of 267, 507 using Euclid's algorithm
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, 507 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 267, 507 is 3 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, 507 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, 507 is 3.
HCF(267, 507) = 3
HCF of 267, 507 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 267, 507 is 3.
Highest Common Factor of 267,507 is 3
Step 1: Since 507 > 267, we apply the division lemma to 507 and 267, to get
507 = 267 x 1 + 240
Step 2: Since the reminder 267 ≠ 0, we apply division lemma to 240 and 267, to get
267 = 240 x 1 + 27
Step 3: We consider the new divisor 240 and the new remainder 27, and apply the division lemma to get
240 = 27 x 8 + 24
We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get
27 = 24 x 1 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 267 and 507 is 3
Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(240,27) = HCF(267,240) = HCF(507,267) .
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Frequently Asked Questions on HCF of 267, 507 using Euclid's Algorithm
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, 507?
Answer: HCF of 267, 507 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 267, 507 using Euclid's Algorithm?
Answer: For arbitrary numbers 267, 507 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.