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 669, 869, 840 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 669, 869, 840 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 669, 869, 840 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 669, 869, 840 is 1.
HCF(669, 869, 840) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 669, 869, 840 is 1.
Step 1: Since 869 > 669, we apply the division lemma to 869 and 669, to get
869 = 669 x 1 + 200
Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 200 and 669, to get
669 = 200 x 3 + 69
Step 3: We consider the new divisor 200 and the new remainder 69, and apply the division lemma to get
200 = 69 x 2 + 62
We consider the new divisor 69 and the new remainder 62,and apply the division lemma to get
69 = 62 x 1 + 7
We consider the new divisor 62 and the new remainder 7,and apply the division lemma to get
62 = 7 x 8 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 669 and 869 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(62,7) = HCF(69,62) = HCF(200,69) = HCF(669,200) = HCF(869,669) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 840 > 1, we apply the division lemma to 840 and 1, to get
840 = 1 x 840 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 840 is 1
Notice that 1 = HCF(840,1) .
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 669, 869, 840?
Answer: HCF of 669, 869, 840 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 669, 869, 840 using Euclid's Algorithm?
Answer: For arbitrary numbers 669, 869, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.