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, 820, 507 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 667, 820, 507 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, 820, 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 667, 820, 507 is 1.
HCF(667, 820, 507) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 667, 820, 507 is 1.
Step 1: Since 820 > 667, we apply the division lemma to 820 and 667, to get
820 = 667 x 1 + 153
Step 2: Since the reminder 667 ≠ 0, we apply division lemma to 153 and 667, to get
667 = 153 x 4 + 55
Step 3: We consider the new divisor 153 and the new remainder 55, and apply the division lemma to get
153 = 55 x 2 + 43
We consider the new divisor 55 and the new remainder 43,and apply the division lemma to get
55 = 43 x 1 + 12
We consider the new divisor 43 and the new remainder 12,and apply the division lemma to get
43 = 12 x 3 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
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 667 and 820 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(43,12) = HCF(55,43) = HCF(153,55) = HCF(667,153) = HCF(820,667) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 507 > 1, we apply the division lemma to 507 and 1, to get
507 = 1 x 507 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 507 is 1
Notice that 1 = HCF(507,1) .
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 667, 820, 507?
Answer: HCF of 667, 820, 507 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 667, 820, 507 using Euclid's Algorithm?
Answer: For arbitrary numbers 667, 820, 507 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.