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, 906, 101, 742 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 906, 101, 742 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 357, 906, 101, 742 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, 906, 101, 742 is 1.
HCF(357, 906, 101, 742) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 357, 906, 101, 742 is 1.
Step 1: Since 906 > 357, we apply the division lemma to 906 and 357, to get
906 = 357 x 2 + 192
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 192 and 357, to get
357 = 192 x 1 + 165
Step 3: We consider the new divisor 192 and the new remainder 165, and apply the division lemma to get
192 = 165 x 1 + 27
We consider the new divisor 165 and the new remainder 27,and apply the division lemma to get
165 = 27 x 6 + 3
We consider the new divisor 27 and the new remainder 3,and apply the division lemma to get
27 = 3 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 357 and 906 is 3
Notice that 3 = HCF(27,3) = HCF(165,27) = HCF(192,165) = HCF(357,192) = HCF(906,357) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 101 > 3, we apply the division lemma to 101 and 3, to get
101 = 3 x 33 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 101 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(101,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 742 > 1, we apply the division lemma to 742 and 1, to get
742 = 1 x 742 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 742 is 1
Notice that 1 = HCF(742,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 906, 101, 742?
Answer: HCF of 357, 906, 101, 742 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 906, 101, 742 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 906, 101, 742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.