Highest Common Factor of 357, 840, 266 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 357, 840, 266 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 840, 266 is 7 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 357, 840, 266 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 357, 840, 266 is 7.
HCF(357, 840, 266) = 7
HCF of 357, 840, 266 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 357, 840, 266 is 7.
Highest Common Factor of 357,840,266 is 7
Step 1: Since 840 > 357, we apply the division lemma to 840 and 357, to get
840 = 357 x 2 + 126
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 126 and 357, to get
357 = 126 x 2 + 105
Step 3: We consider the new divisor 126 and the new remainder 105, and apply the division lemma to get
126 = 105 x 1 + 21
We consider the new divisor 105 and the new remainder 21, and apply the division lemma to get
105 = 21 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 357 and 840 is 21
Notice that 21 = HCF(105,21) = HCF(126,105) = HCF(357,126) = HCF(840,357) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 266 > 21, we apply the division lemma to 266 and 21, to get
266 = 21 x 12 + 14
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 14 and 21, to get
21 = 14 x 1 + 7
Step 3: We consider the new divisor 14 and the new remainder 7, and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 21 and 266 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(266,21) .
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Frequently Asked Questions on HCF of 357, 840, 266 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 357, 840, 266?
Answer: HCF of 357, 840, 266 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 840, 266 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 840, 266 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.