Highest Common Factor of 660, 840 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 660, 840 i.e. 60 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 840 is 60 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 660, 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 660, 840 is 60.
HCF(660, 840) = 60
HCF of 660, 840 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 840 is 60.
Highest Common Factor of 660,840 is 60
Step 1: Since 840 > 660, we apply the division lemma to 840 and 660, to get
840 = 660 x 1 + 180
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 180 and 660, to get
660 = 180 x 3 + 120
Step 3: We consider the new divisor 180 and the new remainder 120, and apply the division lemma to get
180 = 120 x 1 + 60
We consider the new divisor 120 and the new remainder 60, and apply the division lemma to get
120 = 60 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 60, the HCF of 660 and 840 is 60
Notice that 60 = HCF(120,60) = HCF(180,120) = HCF(660,180) = HCF(840,660) .
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Frequently Asked Questions on HCF of 660, 840 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 660, 840?
Answer: HCF of 660, 840 is 60 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 840 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
