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 672, 473, 841 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 672, 473, 841 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 672, 473, 841 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 672, 473, 841 is 1.
HCF(672, 473, 841) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 672, 473, 841 is 1.
Step 1: Since 672 > 473, we apply the division lemma to 672 and 473, to get
672 = 473 x 1 + 199
Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 199 and 473, to get
473 = 199 x 2 + 75
Step 3: We consider the new divisor 199 and the new remainder 75, and apply the division lemma to get
199 = 75 x 2 + 49
We consider the new divisor 75 and the new remainder 49,and apply the division lemma to get
75 = 49 x 1 + 26
We consider the new divisor 49 and the new remainder 26,and apply the division lemma to get
49 = 26 x 1 + 23
We consider the new divisor 26 and the new remainder 23,and apply the division lemma to get
26 = 23 x 1 + 3
We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get
23 = 3 x 7 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 672 and 473 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(26,23) = HCF(49,26) = HCF(75,49) = HCF(199,75) = HCF(473,199) = HCF(672,473) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 841 > 1, we apply the division lemma to 841 and 1, to get
841 = 1 x 841 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 841 is 1
Notice that 1 = HCF(841,1) .
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 672, 473, 841?
Answer: HCF of 672, 473, 841 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 672, 473, 841 using Euclid's Algorithm?
Answer: For arbitrary numbers 672, 473, 841 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.