Highest Common Factor of 945, 399, 657 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 945, 399, 657 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 945, 399, 657 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 945, 399, 657 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 945, 399, 657 is 3.
HCF(945, 399, 657) = 3
HCF of 945, 399, 657 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 945, 399, 657 is 3.
Highest Common Factor of 945,399,657 is 3
Step 1: Since 945 > 399, we apply the division lemma to 945 and 399, to get
945 = 399 x 2 + 147
Step 2: Since the reminder 399 ≠ 0, we apply division lemma to 147 and 399, to get
399 = 147 x 2 + 105
Step 3: We consider the new divisor 147 and the new remainder 105, and apply the division lemma to get
147 = 105 x 1 + 42
We consider the new divisor 105 and the new remainder 42,and apply the division lemma to get
105 = 42 x 2 + 21
We consider the new divisor 42 and the new remainder 21,and apply the division lemma to get
42 = 21 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 945 and 399 is 21
Notice that 21 = HCF(42,21) = HCF(105,42) = HCF(147,105) = HCF(399,147) = HCF(945,399) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 657 > 21, we apply the division lemma to 657 and 21, to get
657 = 21 x 31 + 6
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 6 and 21, to get
21 = 6 x 3 + 3
Step 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 21 and 657 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(657,21) .
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Frequently Asked Questions on HCF of 945, 399, 657 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 945, 399, 657?
Answer: HCF of 945, 399, 657 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 945, 399, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 945, 399, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.