Highest Common Factor of 667, 252 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 667, 252 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 667, 252 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 667, 252 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 667, 252 is 1.
HCF(667, 252) = 1
HCF of 667, 252 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 667, 252 is 1.
Highest Common Factor of 667,252 is 1
Step 1: Since 667 > 252, we apply the division lemma to 667 and 252, to get
667 = 252 x 2 + 163
Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 163 and 252, to get
252 = 163 x 1 + 89
Step 3: We consider the new divisor 163 and the new remainder 89, and apply the division lemma to get
163 = 89 x 1 + 74
We consider the new divisor 89 and the new remainder 74,and apply the division lemma to get
89 = 74 x 1 + 15
We consider the new divisor 74 and the new remainder 15,and apply the division lemma to get
74 = 15 x 4 + 14
We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get
15 = 14 x 1 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 667 and 252 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(74,15) = HCF(89,74) = HCF(163,89) = HCF(252,163) = HCF(667,252) .
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Frequently Asked Questions on HCF of 667, 252 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 667, 252?
Answer: HCF of 667, 252 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 667, 252 using Euclid's Algorithm?
Answer: For arbitrary numbers 667, 252 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.