Highest Common Factor of 840, 495, 87 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, 495, 87 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 840, 495, 87 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, 495, 87 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, 495, 87 is 3.
HCF(840, 495, 87) = 3
HCF of 840, 495, 87 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, 495, 87 is 3.
Highest Common Factor of 840,495,87 is 3
Step 1: Since 840 > 495, we apply the division lemma to 840 and 495, to get
840 = 495 x 1 + 345
Step 2: Since the reminder 495 ≠ 0, we apply division lemma to 345 and 495, to get
495 = 345 x 1 + 150
Step 3: We consider the new divisor 345 and the new remainder 150, and apply the division lemma to get
345 = 150 x 2 + 45
We consider the new divisor 150 and the new remainder 45,and apply the division lemma to get
150 = 45 x 3 + 15
We consider the new divisor 45 and the new remainder 15,and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 840 and 495 is 15
Notice that 15 = HCF(45,15) = HCF(150,45) = HCF(345,150) = HCF(495,345) = HCF(840,495) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 87 > 15, we apply the division lemma to 87 and 15, to get
87 = 15 x 5 + 12
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 12 and 15, to get
15 = 12 x 1 + 3
Step 3: We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 87 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(87,15) .
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Frequently Asked Questions on HCF of 840, 495, 87 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, 495, 87?
Answer: HCF of 840, 495, 87 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 840, 495, 87 using Euclid's Algorithm?
Answer: For arbitrary numbers 840, 495, 87 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.