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 358, 946, 136 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 358, 946, 136 is 2 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 358, 946, 136 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 358, 946, 136 is 2.
HCF(358, 946, 136) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 358, 946, 136 is 2.
Step 1: Since 946 > 358, we apply the division lemma to 946 and 358, to get
946 = 358 x 2 + 230
Step 2: Since the reminder 358 ≠ 0, we apply division lemma to 230 and 358, to get
358 = 230 x 1 + 128
Step 3: We consider the new divisor 230 and the new remainder 128, and apply the division lemma to get
230 = 128 x 1 + 102
We consider the new divisor 128 and the new remainder 102,and apply the division lemma to get
128 = 102 x 1 + 26
We consider the new divisor 102 and the new remainder 26,and apply the division lemma to get
102 = 26 x 3 + 24
We consider the new divisor 26 and the new remainder 24,and apply the division lemma to get
26 = 24 x 1 + 2
We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 358 and 946 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(102,26) = HCF(128,102) = HCF(230,128) = HCF(358,230) = HCF(946,358) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 136 > 2, we apply the division lemma to 136 and 2, to get
136 = 2 x 68 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 136 is 2
Notice that 2 = HCF(136,2) .
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 358, 946, 136?
Answer: HCF of 358, 946, 136 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 358, 946, 136 using Euclid's Algorithm?
Answer: For arbitrary numbers 358, 946, 136 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.