Highest Common Factor of 745, 420, 667 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 745, 420, 667 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 745, 420, 667 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 745, 420, 667 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 745, 420, 667 is 1.
HCF(745, 420, 667) = 1
HCF of 745, 420, 667 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 745, 420, 667 is 1.
Highest Common Factor of 745,420,667 is 1
Step 1: Since 745 > 420, we apply the division lemma to 745 and 420, to get
745 = 420 x 1 + 325
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 325 and 420, to get
420 = 325 x 1 + 95
Step 3: We consider the new divisor 325 and the new remainder 95, and apply the division lemma to get
325 = 95 x 3 + 40
We consider the new divisor 95 and the new remainder 40,and apply the division lemma to get
95 = 40 x 2 + 15
We consider the new divisor 40 and the new remainder 15,and apply the division lemma to get
40 = 15 x 2 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 745 and 420 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(95,40) = HCF(325,95) = HCF(420,325) = HCF(745,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 667 > 5, we apply the division lemma to 667 and 5, to get
667 = 5 x 133 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 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 5 and 667 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(667,5) .
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Frequently Asked Questions on HCF of 745, 420, 667 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 745, 420, 667?
Answer: HCF of 745, 420, 667 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 745, 420, 667 using Euclid's Algorithm?
Answer: For arbitrary numbers 745, 420, 667 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.