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, 753, 639 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 669, 753, 639 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 669, 753, 639 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, 753, 639 is 3.
HCF(669, 753, 639) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 669, 753, 639 is 3.
Step 1: Since 753 > 669, we apply the division lemma to 753 and 669, to get
753 = 669 x 1 + 84
Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 84 and 669, to get
669 = 84 x 7 + 81
Step 3: We consider the new divisor 84 and the new remainder 81, and apply the division lemma to get
84 = 81 x 1 + 3
We consider the new divisor 81 and the new remainder 3, and apply the division lemma to get
81 = 3 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 669 and 753 is 3
Notice that 3 = HCF(81,3) = HCF(84,81) = HCF(669,84) = HCF(753,669) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 639 > 3, we apply the division lemma to 639 and 3, to get
639 = 3 x 213 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 639 is 3
Notice that 3 = HCF(639,3) .
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, 753, 639?
Answer: HCF of 669, 753, 639 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 669, 753, 639 using Euclid's Algorithm?
Answer: For arbitrary numbers 669, 753, 639 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.