Highest Common Factor of 840, 672, 537 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 840, 672, 537 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 840, 672, 537 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 840, 672, 537 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 840, 672, 537 is 3.
HCF(840, 672, 537) = 3
HCF of 840, 672, 537 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 840, 672, 537 is 3.
Highest Common Factor of 840,672,537 is 3
Step 1: Since 840 > 672, we apply the division lemma to 840 and 672, to get
840 = 672 x 1 + 168
Step 2: Since the reminder 672 ≠ 0, we apply division lemma to 168 and 672, to get
672 = 168 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 168, the HCF of 840 and 672 is 168
Notice that 168 = HCF(672,168) = HCF(840,672) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 537 > 168, we apply the division lemma to 537 and 168, to get
537 = 168 x 3 + 33
Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 33 and 168, to get
168 = 33 x 5 + 3
Step 3: We consider the new divisor 33 and the new remainder 3, and apply the division lemma to get
33 = 3 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 168 and 537 is 3
Notice that 3 = HCF(33,3) = HCF(168,33) = HCF(537,168) .
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Frequently Asked Questions on HCF of 840, 672, 537 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 840, 672, 537?
Answer: HCF of 840, 672, 537 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 840, 672, 537 using Euclid's Algorithm?
Answer: For arbitrary numbers 840, 672, 537 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.