Highest Common Factor of 351, 945, 669 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 351, 945, 669 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 351, 945, 669 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 351, 945, 669 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 351, 945, 669 is 3.
HCF(351, 945, 669) = 3
HCF of 351, 945, 669 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 351, 945, 669 is 3.
Highest Common Factor of 351,945,669 is 3
Step 1: Since 945 > 351, we apply the division lemma to 945 and 351, to get
945 = 351 x 2 + 243
Step 2: Since the reminder 351 ≠ 0, we apply division lemma to 243 and 351, to get
351 = 243 x 1 + 108
Step 3: We consider the new divisor 243 and the new remainder 108, and apply the division lemma to get
243 = 108 x 2 + 27
We consider the new divisor 108 and the new remainder 27, and apply the division lemma to get
108 = 27 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 351 and 945 is 27
Notice that 27 = HCF(108,27) = HCF(243,108) = HCF(351,243) = HCF(945,351) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 669 > 27, we apply the division lemma to 669 and 27, to get
669 = 27 x 24 + 21
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 21 and 27, to get
27 = 21 x 1 + 6
Step 3: We consider the new divisor 21 and the new remainder 6, and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3, and apply the division lemma 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 27 and 669 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(669,27) .
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Frequently Asked Questions on HCF of 351, 945, 669 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 351, 945, 669?
Answer: HCF of 351, 945, 669 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 351, 945, 669 using Euclid's Algorithm?
Answer: For arbitrary numbers 351, 945, 669 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.