Highest Common Factor of 669, 140 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, 140 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 669, 140 is 1 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, 140 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, 140 is 1.
HCF(669, 140) = 1
HCF of 669, 140 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, 140 is 1.
Highest Common Factor of 669,140 is 1
Step 1: Since 669 > 140, we apply the division lemma to 669 and 140, to get
669 = 140 x 4 + 109
Step 2: Since the reminder 140 ≠ 0, we apply division lemma to 109 and 140, to get
140 = 109 x 1 + 31
Step 3: We consider the new divisor 109 and the new remainder 31, and apply the division lemma to get
109 = 31 x 3 + 16
We consider the new divisor 31 and the new remainder 16,and apply the division lemma to get
31 = 16 x 1 + 15
We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get
16 = 15 x 1 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 669 and 140 is 1
Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(31,16) = HCF(109,31) = HCF(140,109) = HCF(669,140) .
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Frequently Asked Questions on HCF of 669, 140 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, 140?
Answer: HCF of 669, 140 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 669, 140 using Euclid's Algorithm?
Answer: For arbitrary numbers 669, 140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
