Highest Common Factor of 669, 120 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 669, 120 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 669, 120 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 669, 120 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 669, 120 is 3.
HCF(669, 120) = 3
HCF of 669, 120 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 669, 120 is 3.
Highest Common Factor of 669,120 is 3
Step 1: Since 669 > 120, we apply the division lemma to 669 and 120, to get
669 = 120 x 5 + 69
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 69 and 120, to get
120 = 69 x 1 + 51
Step 3: We consider the new divisor 69 and the new remainder 51, and apply the division lemma to get
69 = 51 x 1 + 18
We consider the new divisor 51 and the new remainder 18,and apply the division lemma to get
51 = 18 x 2 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 669 and 120 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(51,18) = HCF(69,51) = HCF(120,69) = HCF(669,120) .
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Frequently Asked Questions on HCF of 669, 120 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 669, 120?
Answer: HCF of 669, 120 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 669, 120 using Euclid's Algorithm?
Answer: For arbitrary numbers 669, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.