Highest Common Factor of 357, 1662 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, 1662 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 1662 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 357, 1662 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, 1662 is 3.
HCF(357, 1662) = 3
HCF of 357, 1662 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, 1662 is 3.
Highest Common Factor of 357,1662 is 3
Step 1: Since 1662 > 357, we apply the division lemma to 1662 and 357, to get
1662 = 357 x 4 + 234
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 234 and 357, to get
357 = 234 x 1 + 123
Step 3: We consider the new divisor 234 and the new remainder 123, and apply the division lemma to get
234 = 123 x 1 + 111
We consider the new divisor 123 and the new remainder 111,and apply the division lemma to get
123 = 111 x 1 + 12
We consider the new divisor 111 and the new remainder 12,and apply the division lemma to get
111 = 12 x 9 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 357 and 1662 is 3
Notice that 3 = HCF(12,3) = HCF(111,12) = HCF(123,111) = HCF(234,123) = HCF(357,234) = HCF(1662,357) .
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Frequently Asked Questions on HCF of 357, 1662 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, 1662?
Answer: HCF of 357, 1662 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 1662 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 1662 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.