Highest Common Factor of 269, 970, 604, 705 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 269, 970, 604, 705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 269, 970, 604, 705 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 269, 970, 604, 705 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 269, 970, 604, 705 is 1.
HCF(269, 970, 604, 705) = 1
HCF of 269, 970, 604, 705 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 269, 970, 604, 705 is 1.
Highest Common Factor of 269,970,604,705 is 1
Step 1: Since 970 > 269, we apply the division lemma to 970 and 269, to get
970 = 269 x 3 + 163
Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 163 and 269, to get
269 = 163 x 1 + 106
Step 3: We consider the new divisor 163 and the new remainder 106, and apply the division lemma to get
163 = 106 x 1 + 57
We consider the new divisor 106 and the new remainder 57,and apply the division lemma to get
106 = 57 x 1 + 49
We consider the new divisor 57 and the new remainder 49,and apply the division lemma to get
57 = 49 x 1 + 8
We consider the new divisor 49 and the new remainder 8,and apply the division lemma to get
49 = 8 x 6 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 269 and 970 is 1
Notice that 1 = HCF(8,1) = HCF(49,8) = HCF(57,49) = HCF(106,57) = HCF(163,106) = HCF(269,163) = HCF(970,269) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 604 > 1, we apply the division lemma to 604 and 1, to get
604 = 1 x 604 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 604 is 1
Notice that 1 = HCF(604,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 705 > 1, we apply the division lemma to 705 and 1, to get
705 = 1 x 705 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 705 is 1
Notice that 1 = HCF(705,1) .
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Frequently Asked Questions on HCF of 269, 970, 604, 705 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 269, 970, 604, 705?
Answer: HCF of 269, 970, 604, 705 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 269, 970, 604, 705 using Euclid's Algorithm?
Answer: For arbitrary numbers 269, 970, 604, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.