Highest Common Factor of 60, 690, 966, 621 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 60, 690, 966, 621 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 60, 690, 966, 621 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 60, 690, 966, 621 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 60, 690, 966, 621 is 3.
HCF(60, 690, 966, 621) = 3
HCF of 60, 690, 966, 621 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 60, 690, 966, 621 is 3.
Highest Common Factor of 60,690,966,621 is 3
Step 1: Since 690 > 60, we apply the division lemma to 690 and 60, to get
690 = 60 x 11 + 30
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 30 and 60, to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 60 and 690 is 30
Notice that 30 = HCF(60,30) = HCF(690,60) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 966 > 30, we apply the division lemma to 966 and 30, to get
966 = 30 x 32 + 6
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 6 and 30, to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 30 and 966 is 6
Notice that 6 = HCF(30,6) = HCF(966,30) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 621 > 6, we apply the division lemma to 621 and 6, to get
621 = 6 x 103 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 621 is 3
Notice that 3 = HCF(6,3) = HCF(621,6) .
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Frequently Asked Questions on HCF of 60, 690, 966, 621 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 60, 690, 966, 621?
Answer: HCF of 60, 690, 966, 621 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 60, 690, 966, 621 using Euclid's Algorithm?
Answer: For arbitrary numbers 60, 690, 966, 621 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.